#Loading the Dataset
#Data Description
#The dataset consists of 14710 observations and 8 variables. Each row in dataset represents an employee; each column contains employee attributes:
#Independent Variables were: #Age: Age of employees, #Department: Department of work, #Distance from home, #Education: 1-Below College; 2-College; 3-Bachelor; 4-Master; 5-Doctor; #Education Field #Environment Satisfaction: 1-Low; 2-Medium; 3-High; 4-Very High; #Job Satisfaction: 1-Low; 2-Medium; 3-High; 4-Very High; #Marital Status, #Monthly Income, #Num Companies Worked: Number of companies worked prior to IBM, #Work Life Balance: 1-Bad; 2-Good; 3-Better; 4-Best; #Years At Company: Current years of service in IBM #Dependent Variable was: #Attrition: Employee attrition status(0 or 1)
library(readr)
library(MVA)
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library(caTools)
attr <- read_csv("/Users/meet/Desktop/Attrition Data copy.csv")
## Rows: 1470 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): Department, MaritalStatus, EducationField, Attrition
## dbl (10): Sr.no, Education, DistanceFromHome, EnvironmentSatisfaction, JobSa...
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attr_new <- attr[,c(6:14)]
str(attr_new)
## tibble [1,470 × 9] (S3: tbl_df/tbl/data.frame)
## $ Education : num [1:1470] 2 1 2 4 1 2 3 1 3 3 ...
## $ DistanceFromHome : num [1:1470] 1 8 2 3 2 2 3 24 23 27 ...
## $ EnvironmentSatisfaction: num [1:1470] 2 3 4 4 1 4 3 4 4 3 ...
## $ JobSatisfaction : num [1:1470] 4 2 3 3 2 4 1 3 3 3 ...
## $ Age : num [1:1470] 41 49 37 33 27 32 59 30 38 36 ...
## $ MonthlyIncome : num [1:1470] 5993 5130 2090 2909 3468 ...
## $ NumCompaniesWorked : num [1:1470] 8 1 6 1 9 0 4 1 0 6 ...
## $ WorkLifeBalance : num [1:1470] 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : num [1:1470] 6 10 0 8 2 7 1 1 9 7 ...
corrplot(cor(attr_new), type = "upper", method = "color")
#The correlation matrix shows us that there is correlation between the columns in both cases.
#Hence, Principal Component Analysis (PCA) can be used to reduce the number of columns for the analysis.
result<-cor(attr_new)
result
## Education DistanceFromHome EnvironmentSatisfaction
## Education 1.000000000 0.021041826 -0.027128313
## DistanceFromHome 0.021041826 1.000000000 -0.016075327
## EnvironmentSatisfaction -0.027128313 -0.016075327 1.000000000
## JobSatisfaction -0.011296117 -0.003668839 -0.006784353
## Age 0.208033731 -0.001686120 0.010146428
## MonthlyIncome 0.094960677 -0.017014445 -0.006259088
## NumCompaniesWorked 0.126316560 -0.029250804 0.012594323
## WorkLifeBalance 0.009819189 -0.026556004 0.027627295
## YearsAtCompany 0.069113696 0.009507720 0.001457549
## JobSatisfaction Age MonthlyIncome
## Education -0.011296117 0.208033731 0.094960677
## DistanceFromHome -0.003668839 -0.001686120 -0.017014445
## EnvironmentSatisfaction -0.006784353 0.010146428 -0.006259088
## JobSatisfaction 1.000000000 -0.004891877 -0.007156742
## Age -0.004891877 1.000000000 0.497854567
## MonthlyIncome -0.007156742 0.497854567 1.000000000
## NumCompaniesWorked -0.055699426 0.299634758 0.149515216
## WorkLifeBalance -0.019458710 -0.021490028 0.030683082
## YearsAtCompany -0.003802628 0.311308770 0.514284826
## NumCompaniesWorked WorkLifeBalance YearsAtCompany
## Education 0.126316560 0.009819189 0.069113696
## DistanceFromHome -0.029250804 -0.026556004 0.009507720
## EnvironmentSatisfaction 0.012594323 0.027627295 0.001457549
## JobSatisfaction -0.055699426 -0.019458710 -0.003802628
## Age 0.299634758 -0.021490028 0.311308770
## MonthlyIncome 0.149515216 0.030683082 0.514284826
## NumCompaniesWorked 1.000000000 -0.008365685 -0.118421340
## WorkLifeBalance -0.008365685 1.000000000 0.012089185
## YearsAtCompany -0.118421340 0.012089185 1.000000000
#Principal Component Analysis
attr_pca <- prcomp(attr_new,scale=TRUE)
attr_pca
## Standard deviations (1, .., p=9):
## [1] 1.4107854 1.0961163 1.0284243 1.0017232 0.9918265 0.9858032 0.9380353
## [8] 0.7089431 0.6395853
##
## Rotation (n x k) = (9 x 9):
## PC1 PC2 PC3 PC4
## Education 2.381768e-01 -0.35557851 -0.197280301 0.09516238
## DistanceFromHome -8.671733e-03 0.06435091 -0.514604455 0.57141436
## EnvironmentSatisfaction -9.815712e-05 -0.01048877 0.543287792 -0.07285182
## JobSatisfaction -2.501490e-02 0.19635694 -0.243998413 -0.73787765
## Age 5.648580e-01 -0.17188575 -0.031031680 -0.07449252
## MonthlyIncome 5.879270e-01 0.18877561 0.051145765 -0.01437114
## NumCompaniesWorked 2.352160e-01 -0.70653759 0.053680763 -0.10519118
## WorkLifeBalance 1.281059e-02 0.06095915 0.578824064 0.30375136
## YearsAtCompany 4.715480e-01 0.51250805 0.008252963 0.07465387
## PC5 PC6 PC7 PC8
## Education 0.147310191 0.380586266 0.7648985 0.10135538
## DistanceFromHome -0.413127157 0.387344497 -0.2884104 0.01656602
## EnvironmentSatisfaction -0.792975712 0.147162364 0.2195899 0.01206021
## JobSatisfaction -0.038278906 0.572850578 -0.1554622 0.05360003
## Age -0.063514430 0.001825971 -0.1136350 -0.73608470
## MonthlyIncome 0.005456455 -0.070320656 -0.1458130 0.12629670
## NumCompaniesWorked -0.056606187 -0.021737738 -0.3990416 0.48889329
## WorkLifeBalance 0.412404321 0.586824005 -0.2253115 -0.04159593
## YearsAtCompany 0.002113045 -0.074300192 0.1232388 0.43349260
## PC9
## Education -0.08349607
## DistanceFromHome -0.01693693
## EnvironmentSatisfaction -0.02425999
## JobSatisfaction 0.01245128
## Age 0.29344102
## MonthlyIncome -0.75742732
## NumCompaniesWorked 0.17205718
## WorkLifeBalance 0.04338735
## YearsAtCompany 0.54836854
summary(attr_pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4108 1.0961 1.0284 1.0017 0.9918 0.9858 0.93804
## Proportion of Variance 0.2212 0.1335 0.1175 0.1115 0.1093 0.1080 0.09777
## Cumulative Proportion 0.2212 0.3546 0.4722 0.5837 0.6930 0.8009 0.89870
## PC8 PC9
## Standard deviation 0.70894 0.63959
## Proportion of Variance 0.05584 0.04545
## Cumulative Proportion 0.95455 1.00000
#Scree diagram
fviz_eig(attr_pca, addlabels = TRUE)
# The scree diagram shows us that sum of the first 2 principal components is less than 70%.
# So, we cannot move forward using PCA for column reduction.
# We now move on to check EFA for this main dataset.
pca_data <- as.data.frame(attr_pca$x)
pca_data <- pca_data[,1:2]
#Exploratory Factor Analysis (EFA)
fit.attr <- principal(attr[,6:14], nfactors=5, rotate="varimax")
fa.diagram(fit.attr)
# Defining the factors obtained
# RC1
# All of them YearsAtCompany, MonthlyIncome and Age are popular factors among all employees in terms of attrition.
# RC2
# NumCompaniesWorked and Education are popular factors.
# RC3
# It has only 1 factor DistanceFromHome
# RC4
# Both factors JobSatisfaction and WorkLifeBalance are important in terms of attrition for employees
# RC5
# RC5 has only one variable, Enviornment Satisfaction.
# Defining new columns through EFA
efa_data <- as.data.frame(fit.attr$scores)
efa_data
## RC1 RC2 RC4 RC3 RC5
## 1 -0.417720371 1.420684382 -2.6196400200 -0.669024391 -0.0639742397
## 2 0.590433801 -0.815885321 0.5428254314 -0.115196832 0.6302573269
## 3 -1.156384919 0.694986263 -0.0622469420 -1.167435276 1.4640304453
## 4 -0.246767057 -0.337471126 0.1057013656 -0.622696488 0.7333091064
## 5 -1.436474293 0.869471891 0.6333471330 -1.145848511 -0.8327594849
## 6 -0.306523556 -1.263860792 -1.5754649157 -0.659057596 1.1588009984
## 7 -0.407765702 1.702249017 0.1884392202 0.099862209 0.5532967795
## 8 -0.888319480 -1.319977699 0.0429559225 1.300085494 1.4119239983
## 9 0.726937482 -0.837508813 0.1106768804 1.415601272 0.9597903899
## 10 -0.351744429 0.873980567 -0.8439631970 2.099078463 0.4422761251
## 11 -0.492509995 -0.602149493 0.7346274232 0.902709119 -1.6618589133
## 12 -0.070091733 -1.547233238 0.1037839246 0.525189210 1.1016490751
## 13 -0.627162329 -1.194609919 -0.8891879465 1.974204668 -1.1517957072
## 14 -0.631762262 -1.127165298 -0.6155303133 0.585105278 -0.6327836917
## 15 -1.028625081 0.278666178 0.1386493947 1.335234324 0.2687651726
## 16 0.380989017 -0.293026351 1.5320521291 1.765855782 -0.9422563891
## 17 -0.507431955 -0.919876982 -0.2569410317 0.131761085 -1.3912928620
## 18 -1.162360489 -1.153395426 -1.4811517968 0.754608888 1.1906202033
## 19 2.920207664 0.011946448 -0.6182992384 -1.069594386 -1.8222467339
## 20 -0.598792189 0.625433138 -0.6668809267 -1.301673230 1.1589593405
## 21 -0.796798119 -1.238424806 -0.8393231325 0.484765262 -1.4577204447
## 22 -0.808991578 1.671203312 1.3851302733 0.275392737 0.2596364336
## 23 0.954859410 -0.467449622 0.8058752461 0.012528810 -1.8929415675
## 24 -1.385266113 -1.284852769 -0.5395200630 0.144759501 0.2231654969
## 25 -0.708141174 -0.715133185 1.2782321252 -0.139807732 -0.2244610261
## 26 2.160528814 0.843943298 -0.9812854269 -0.243415367 0.4343589008
## 27 -0.098040274 -1.324103368 1.3565592169 1.016135987 -0.3025687513
## 28 0.494270441 -0.161976173 0.7232616181 0.169598738 -0.0931712390
## 29 1.846513042 0.019154885 -0.5587079072 -0.549502758 -1.8224393056
## 30 0.865163254 1.464352183 0.3712498398 -0.017086016 -0.6146976370
## 31 -1.018059407 0.296128835 -0.6368427209 -1.285263029 0.2094997409
## 32 0.172020498 0.227461082 0.3167976069 -0.748604908 0.7588313949
## 33 -0.216018289 -1.293120858 0.0736721826 -0.130037276 1.1398716805
## 34 -0.714760010 0.045755318 0.2740107452 -1.395650227 0.9913957405
## 35 -1.208016725 -0.388201033 -1.5054616710 -0.828391794 -0.7397390341
## 36 -0.279289523 -0.424758232 -1.0173097782 -0.450587734 1.3153401392
## 37 -0.205089165 -0.150139220 -0.1345687309 -0.918526525 -1.3516922446
## 38 -0.723580326 -0.485601458 -0.6393384461 -1.137545543 0.9471748315
## 39 -1.211750071 2.241525542 2.2941323294 -0.774884649 -0.5875760421
## 40 -0.427288345 -0.055640731 1.3624215802 -0.488543372 0.2164290333
## 41 -0.821757834 -0.784708348 -0.6790839484 -1.040618160 0.2905896503
## 42 -1.164301048 -0.049511572 1.4339592252 -0.240270055 0.8076585608
## 43 -1.188969993 -0.466797044 -0.7895924627 2.016098760 -1.5938410235
## 44 0.223708922 -0.936338594 0.1451625830 -0.210248883 0.9327499819
## 45 0.135957920 -1.409580713 -0.5975597980 -1.274304878 0.2135094111
## 46 2.749745284 -0.848907348 0.1250560935 0.191237414 -0.7706313697
## 47 0.087008093 -0.581774146 0.1705889746 1.507286841 -1.0501878314
## 48 -0.914875226 0.263669800 0.6601251431 0.958799019 -0.3398476073
## 49 0.329279536 0.875932835 -0.6493488286 -0.884236928 -1.7155505044
## 50 -0.759701820 -1.197855870 -0.7057667537 -0.682811858 1.3881742059
## 51 -0.651972121 1.951937521 -0.1524630491 -1.480113437 -0.9586771926
## 52 -0.941188725 -0.066903406 -0.8194797612 0.004458204 -0.0580716434
## 53 -0.445838139 2.091993318 0.3973510562 0.019574254 -0.7982592163
## 54 0.006811399 -0.306264025 1.3431138331 0.444196069 0.4699180583
## 55 -1.203324368 0.885953499 -1.4621022833 1.333910411 0.4143245099
## 56 1.347009233 -1.289484269 -0.5892197906 -1.370046176 -1.5102356981
## 57 0.309043763 0.499469417 0.5640077787 2.014551881 -1.0420753249
## 58 -0.770271383 0.694431062 1.4382863967 1.895110663 0.0875111524
## 59 -0.244423048 0.218634727 -1.4730007629 -0.087723792 0.8806126261
## 60 0.104310636 -0.181227819 1.0136173251 -1.425162988 -1.9478507751
## 61 0.110147253 -0.755564195 -0.5821789819 -1.274744052 -1.7254938860
## 62 0.115192886 -0.059416842 -0.4607012579 1.991337699 0.5160082985
## 63 3.054557696 0.094601237 -0.9412550944 -0.052857613 -0.2595631344
## 64 1.569371892 1.660852928 0.3436600976 2.434991813 -1.1223256463
## 65 1.283715752 -0.909396839 0.1104803701 -0.177630388 0.0704654919
## 66 1.270508162 0.546157592 -0.0828619765 -0.360479026 1.1765870566
## 67 -0.038641898 -0.338965697 0.7218507066 0.324196536 -0.7252674198
## 68 0.017272475 0.596175924 1.2783505581 0.048972668 -0.5566465648
## 69 -1.048174308 0.789396930 0.3783343160 -0.091154323 -0.4718508262
## 70 -0.692525436 -0.409941701 -0.9113397804 0.387807204 1.0395109946
## 71 -0.003457965 1.497976539 -1.2067280920 -0.985521523 -0.7105318348
## 72 -0.641249602 -0.841741366 0.7398751077 -0.549918444 0.0511587184
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## 74 0.127112603 -0.625545436 0.7382305365 -0.702731588 -0.7755502348
## 75 -0.825243544 0.172457674 -0.6443779583 -0.846795498 -0.6955116028
## 76 0.124047740 -0.610276798 -0.5049093527 -0.363814419 -0.2001850231
## 77 0.481598234 -0.564898784 1.4340619535 -0.225635579 -0.1366216867
## 78 0.255506161 1.323129291 2.2606967653 -0.533217472 1.0141535896
## 79 0.505097869 0.717708446 1.0317124192 -0.981913464 -1.7636969834
## 80 -0.457518402 1.548302120 0.5495334208 -0.689837078 -0.1146051320
## 81 0.024726523 -1.556823805 -1.5894420857 -0.880561831 1.4026923604
## 82 -0.391418260 -0.475557508 0.0324355651 -0.984963288 -0.7883629488
## 83 0.428026656 0.591248996 -0.8360714416 -1.566864871 -1.2326527771
## 84 0.223778996 0.780564831 -0.6162263951 -0.913173976 -0.5416196115
## 85 -0.423162252 -0.689758649 0.6552225005 -0.842371856 -1.4089088475
## 86 0.518603781 1.059977956 -1.7157076894 -0.256560174 1.2934289914
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## 89 0.061742228 -0.999494352 -0.5574882200 -1.089891084 0.0041916217
## 90 0.930069952 -0.687017093 -0.6990270000 -0.507398395 0.3416546731
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## 810 0.081845676 -0.885610433 -0.1659802374 0.061717665 1.0032836673
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## 813 0.348108145 1.685414489 1.3720850051 2.032395634 0.5854591123
## 814 1.301696989 0.701438496 -0.6011614158 -1.374206834 -1.4195293684
## 815 2.655814488 -1.001347747 1.0774667230 -0.080738604 0.0310675781
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## 900 1.147523185 0.113861874 0.8459297874 -1.490225425 -1.3292548043
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## 905 0.926037891 1.278482183 0.2166432832 -2.082629401 1.2359247363
## 906 0.665117352 -0.126686504 -1.4945753126 -0.900743906 1.1130631815
## 907 -0.828390722 -0.487342783 -0.8632659110 1.551766506 0.1559308822
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## 911 -1.294284732 -1.144056277 0.0629839790 -1.052635863 1.1352410879
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## 913 -0.499770484 -1.238248399 -1.5217953176 -0.488400695 0.2915470636
## 914 2.830220620 -0.370437727 0.7224356806 -0.644988882 -1.5593613869
## 915 3.526545544 -1.551646332 0.6131425063 0.038150568 1.4573183936
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## 920 1.070168084 1.916158613 -1.6498812815 0.927391796 1.1958510715
## 921 0.052329371 -0.087510616 1.7170882553 0.660263203 0.1797508335
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## 927 1.853751219 -0.229741510 0.3835287657 -1.304976713 0.7265889729
## 928 0.217111669 1.650357059 0.7505761099 -0.738501292 0.2659065211
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## 943 0.057656479 0.339402207 0.1029540859 0.001698693 0.8705261880
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## 946 0.981468841 1.128949702 1.3251502535 2.211890309 1.3536153575
## 947 0.247179529 0.383962643 0.7754529110 1.876944439 0.9102240110
## 948 0.250435901 2.409014398 -0.3811761228 -0.149927703 -0.1741069633
## 949 0.505795915 -0.187436019 1.5114752539 1.312014754 -0.9286139569
## 950 0.138505109 -1.048774296 0.0283738905 0.763391935 -1.4686272567
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## 952 1.192388124 -1.117101079 0.6939143918 0.266644588 0.3311785460
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## 955 2.447601129 -1.578253150 -0.9503516797 -0.510747382 0.5745516795
## 956 2.742538091 0.146526676 -0.0793398674 -1.076909278 1.4304579705
## 957 1.656134866 2.038129653 0.6148118851 -0.179974048 1.2049092082
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## 960 0.251524483 -0.550224464 -0.6438876970 -1.121168645 0.0714791444
## 961 0.150474488 -0.463653887 1.3197140271 -0.371442810 0.1408139665
## 962 0.010538799 -0.266899957 0.0994954784 -0.540284122 -0.1334479862
## 963 3.410463925 -0.910336076 0.7171401959 -0.127866616 0.1251939105
## 964 -0.029933833 -0.030011882 1.2932266842 -0.527546869 -0.3740353224
## 965 0.259647403 -1.059295193 2.3298662709 0.508883757 0.2953559852
## 966 -0.938683424 -0.988135482 -1.5322284042 0.919750136 1.5145306831
## 967 0.841169475 2.468382046 0.2952258629 0.520613793 0.4604259907
## 968 -0.618876269 0.774278147 0.6756388205 -0.721604353 -0.8325125808
## 969 0.332036550 -0.167967738 0.4514947126 0.694527719 -1.4871560938
## 970 0.913594150 -0.320409626 -0.6885157570 -0.911885261 1.0014236317
## 971 -1.418550828 1.084141508 -0.5732327076 -0.472434788 0.3765437432
## 972 0.825472458 0.534644249 -0.3774180998 0.610813362 1.5356898168
## 973 -1.381180836 -1.174530077 0.4280545620 -1.732626159 0.7774090462
## 974 0.239738379 -1.013681512 -0.6021200151 -1.170361421 0.8747396052
## 975 -0.449364690 -1.144268603 -0.6402452901 -1.372475343 1.4204173174
## 976 1.979009001 1.590062994 -0.9292067115 0.670173103 -1.4648840928
## 977 2.208542587 0.547248803 0.6650167794 1.575035860 1.2562217435
## 978 -0.544406201 -1.255633037 0.0309111131 1.490511481 -1.2201971079
## 979 0.379123187 -0.235637789 -0.0645983084 -1.187377445 -0.1530569895
## 980 -0.133123094 0.110960517 0.1339841442 1.890325217 -0.6289648349
## 981 -1.154561534 0.837302297 0.3160429694 -1.890128940 0.2621422486
## 982 -0.343913156 -0.222646271 -0.8185381595 1.455641096 0.8147047499
## 983 -0.442409515 -0.370442856 0.0202728370 -0.321050929 0.9981721728
## 984 0.747387542 -0.757218120 0.4159296249 -1.488097305 -0.2776080712
## 985 -0.537589775 -0.574206119 1.4827831018 2.232764813 0.1568869045
## 986 0.133085141 -0.365282113 -0.7482805067 1.889608786 0.8196452297
## 987 -0.024214941 0.328790053 0.3891398250 0.343492530 -1.8527919722
## 988 0.572584139 0.602710981 0.5722610947 -0.742384773 -0.5768884155
## 989 -0.028227481 0.203058515 -1.5505721969 1.414030237 1.1667150757
## 990 -0.635078083 0.362134352 -0.0730410511 -1.053657108 0.8249548813
## 991 -0.009720480 -0.177968946 0.2633051844 -1.752793922 -0.2164546834
## 992 -0.647317082 -1.214261855 -0.3167979562 -0.269354949 0.5951991618
## 993 0.454566443 -0.230846531 0.0484173298 1.365487289 0.4684472305
## 994 -0.736047158 -1.017868623 -0.8714699289 1.039625233 -1.1226106876
## 995 1.002749187 0.158932966 -0.9857238969 2.193746355 1.4678439389
## 996 0.985961567 -0.432505423 -1.8446680705 0.615688327 -1.5173924324
## 997 -0.261241346 -0.940034663 -0.5254387925 -0.270304068 0.9011100782
## 998 -0.454631786 -0.599865022 0.1963129004 0.883710987 0.7086987023
## 999 -0.636644254 -1.774765392 -0.6366019595 -1.325934740 -1.3588900687
## 1000 2.333482805 -0.827857534 1.4153249080 0.583388369 0.1405471579
## 1001 -0.628299702 3.086849692 -0.6430690389 1.057816201 0.6084320069
## 1002 -0.683419138 0.507424773 0.0271168594 -0.087666386 -1.4854461062
## 1003 -0.061618510 -0.555629559 -0.6172057381 0.364546560 0.3685552190
## 1004 -1.140134817 0.161836114 -1.5140179675 -0.925812096 -1.5173120138
## 1005 -0.518463033 -0.940452057 1.4474871275 0.269548552 0.0694926370
## 1006 0.114166811 -0.503125629 0.5283846537 1.755562207 -0.6539486423
## 1007 -0.160264433 0.429400387 1.2693616961 2.216492571 -1.1647635620
## 1008 0.198740159 -1.914328018 -0.5955223999 0.001276077 0.4155512389
## 1009 2.462309616 1.000665732 -1.6430980333 -0.930693933 1.3388325941
## 1010 2.008180210 1.006414311 1.2113657801 -0.612399495 1.3093979121
## 1011 1.499928823 0.653860715 0.2308373310 -1.803755225 -0.9307744952
## 1012 -0.013703814 0.668134265 0.7322251332 -0.573484854 -1.7142409263
## 1013 -1.082642889 -0.048151294 0.0802200011 -0.926494374 -1.0066428730
## 1014 -1.015807885 1.523039966 1.4214641018 0.057800818 1.1168344578
## 1015 0.426287849 0.819872656 1.7813619968 -0.513187352 -2.0034885350
## 1016 -0.872625106 1.113438567 1.3773923082 -0.486005032 1.0272434016
## 1017 -1.061642238 -0.464507256 1.6638510700 -0.502639390 -1.7085255823
## 1018 -0.720655411 -1.709367712 2.3036583327 0.006009542 -0.4466331243
## 1019 0.208708421 -0.134404567 -1.5056381984 -0.369322650 -1.8398791677
## 1020 -0.646369904 1.141469831 0.4672503825 1.591065380 0.2189526128
## 1021 -0.369250028 1.600450087 -1.6838089408 -1.035426644 -1.2629774272
## 1022 -1.009091369 -0.333360919 1.3946826508 0.196334657 -1.3081600505
## 1023 -0.326945682 -0.747404255 -1.8977087470 0.383819295 0.4377255291
## 1024 -0.157671630 0.369043320 2.0681926217 -1.116681323 -1.2790893841
## 1025 2.453721063 0.221360473 1.0118062766 -1.379892297 -1.8216071311
## 1026 -0.635943869 -1.634894139 0.0472980343 -0.808850052 1.3484956463
## 1027 -0.214912867 1.034903045 -1.4486951843 -0.094244356 0.7443788017
## 1028 -0.783903641 0.762780460 -0.2618804181 -0.350173214 1.2828409196
## 1029 -0.581613921 0.966867630 -0.8795357995 0.050710885 -1.0444169911
## 1030 0.020886846 0.291751210 1.0105215855 -0.582548523 -0.0832304429
## 1031 0.876231408 -1.317637658 -0.5656648308 -0.615714850 -1.5149612346
## 1032 0.663647562 0.450510946 0.2691845994 -1.087173125 -1.5558715821
## 1033 -0.702288098 0.220808317 2.2414232098 -0.938360912 -1.5740105229
## 1034 0.219892160 0.052405362 0.8313670170 -0.516011290 -0.3298358412
## 1035 0.651793083 0.309139568 1.3476644570 1.483882278 -0.5723396581
## 1036 -1.299505697 1.209287323 0.6653291527 -0.337931489 1.6039811621
## 1037 -1.164166010 1.064974096 -2.5125395814 -0.405600327 -0.4192254214
## 1038 0.285545991 0.485082328 0.3225921408 1.042230263 -0.6510318400
## 1039 -0.311822272 1.110591502 1.2442049295 0.034304092 0.4166380122
## 1040 -0.777137628 0.037510999 0.0883919420 -0.096936624 -1.8623668120
## 1041 1.013598159 -0.807752508 0.6263624225 -0.206617224 1.5390512739
## 1042 -0.142431834 -0.773841358 1.4283849550 0.015438000 0.9827213306
## 1043 -0.260817172 0.362731261 -0.0349553993 -0.633504613 0.2458172743
## 1044 1.470583396 1.116601131 -0.3592504665 -0.296642501 1.3647498877
## 1045 0.002020256 0.996789216 -0.9786868567 -0.111706187 -1.6430363761
## 1046 -0.501791481 -0.113049927 0.9256130119 -1.411852578 0.0975031207
## 1047 -0.191379945 0.035071300 -0.2679967563 1.825647125 1.1599038339
## 1048 -0.459385680 -0.588391558 1.3819445332 0.250031123 1.0039244295
## 1049 0.176939554 -0.148331618 1.3913952438 -0.215798112 1.1092377438
## 1050 -1.057990241 0.648061559 -0.9397676877 0.650271446 1.8306442335
## 1051 0.452588914 -0.936255461 -0.6693395843 -0.467954294 -1.4706888991
## 1052 -0.808291356 2.558094993 -0.9391772109 -0.642527577 -1.6436678328
## 1053 -1.160801208 -0.344139869 -0.8788527016 0.137828957 0.1679167231
## 1054 0.974896142 -0.389007532 -1.0946823466 -0.527791767 -0.4385944364
## 1055 0.795884832 0.936773044 0.6592809491 -0.098886541 0.1070285911
## 1056 1.108072012 1.127430596 0.5009678952 1.266486524 -0.3274681910
## 1057 -0.915211357 -0.211774077 1.0137520782 -1.592630996 -1.6764365819
## 1058 -0.808112358 0.829782121 -1.1270761050 1.343182961 -1.2801877824
## 1059 0.605206193 -0.865786461 1.8019939800 1.430831293 -2.0007479044
## 1060 -0.793891588 -1.090610820 -0.0510365131 -0.519438481 1.4260863318
## 1061 -1.411805921 -0.010827140 0.4860837733 0.815637280 -0.6064289444
## 1062 -1.208464805 -1.035104719 0.7524973469 0.494064681 1.1907608478
## 1063 -0.042350671 0.526850113 -1.0762047538 -0.825408429 0.0125722927
## 1064 0.361593444 -0.907127300 0.1674554269 0.953410324 0.0689219709
## 1065 -0.553615991 -1.073059339 1.0155351666 -1.412208387 -0.0666419234
## 1066 0.182045400 0.415799449 -0.0806644778 -0.551499519 0.8366186476
## 1067 -0.919874098 1.804412059 0.7316217283 -0.611306167 -1.5056564955
## 1068 -0.089145067 0.616616753 -0.9727162112 0.802511199 0.3563519285
## 1069 -1.631139133 1.035090074 0.3754354404 -0.191329941 0.7442945000
## 1070 -1.317106209 -0.165256143 -1.8287813178 -0.057036347 -1.5208288013
## 1071 -0.581547549 -0.730296593 1.4217836858 0.229474601 0.0994989861
## 1072 -0.265626028 0.741367298 1.1855039835 -0.467074503 0.6274909024
## 1073 -0.733009361 -1.525492698 0.6514577898 -0.727021297 1.3713322326
## 1074 -0.123827670 -1.377068621 -0.1759364543 2.606938070 0.6253298592
## 1075 -0.638898204 0.642568511 0.1328028496 -0.140763522 0.6201787789
## 1076 0.330503289 -0.546056792 0.3847064385 -0.877296005 0.0394459006
## 1077 2.064550012 0.718600131 -0.6456336770 -0.231234432 -0.8278729238
## 1078 -0.931764815 1.399738189 -0.4601395116 0.445652856 -1.4483831194
## 1079 2.299859908 -0.237176644 2.3927868882 1.926366701 1.1049000572
## 1080 -0.287791901 0.742568722 0.6600785179 -0.380860973 -0.5415569039
## 1081 1.487024837 1.431356941 1.5945992451 -1.299098576 0.4577639308
## 1082 0.447091161 -0.331146889 -1.1182594275 1.905417244 1.1763820104
## 1083 -0.896479817 -1.846628651 0.0981301104 0.886247267 -1.3290432510
## 1084 -0.713452894 1.064095799 -0.5278114304 1.435312794 1.1267243231
## 1085 0.352894575 -0.718329767 0.0683492678 -0.941986229 0.9564635676
## 1086 -0.423019330 -0.402566284 -1.8125233303 0.249241292 1.1108408985
## 1087 3.443524181 -0.419945935 -0.4579918060 1.310923035 -0.3686748127
## 1088 0.019729453 -1.374552960 0.0417237906 -0.341747082 -0.6485095196
## 1089 -0.606532693 0.844363158 0.6124512209 -0.770043901 0.3438435621
## 1090 0.191191416 -0.668978415 -0.5835083801 0.028595968 -1.6993280176
## 1091 -0.002156663 -0.754133206 1.3494800612 0.031067903 0.6827679527
## 1092 -0.360530034 -0.531527238 0.7824407687 1.873976798 1.0227077603
## 1093 -0.280653923 0.441587275 -0.6321338450 1.543809471 1.1538479080
## 1094 1.566337526 -0.358000329 -2.4943992183 -0.109982964 1.1380129843
## 1095 0.226330494 -0.934246875 2.2549673884 -0.153172200 -1.4727105667
## 1096 0.569847362 -0.626504472 0.2182809812 2.053272007 -1.0306846502
## 1097 2.395811948 -1.354317201 -0.5948428415 -0.770990222 0.2694049659
## 1098 -1.172525845 -1.177853332 1.4383157685 1.636594828 0.3093389293
## 1099 -0.473532069 -0.161977751 -0.7023375247 -0.682666882 1.2985071582
## 1100 0.620851476 0.255190390 0.6783120161 -0.657288245 -1.7924490920
## 1101 -0.411969665 -0.406448435 0.1567300688 2.022559233 -1.0282357140
## 1102 -0.224908694 -0.434207954 0.6918919709 -0.423244920 1.3094719569
## 1103 -0.765480244 0.593747905 -1.5534408817 -0.656209428 0.0355789600
## 1104 0.146929331 2.028368732 0.0137454898 0.433567523 0.2991616985
## 1105 -1.370355936 0.911543669 -0.8774946333 0.149701473 0.4097002903
## 1106 -0.759328115 0.821084601 -0.4781967343 1.247547363 -1.5674088185
## 1107 0.354469777 -0.567727457 1.4193300013 -0.458822821 -0.7372774418
## 1108 -0.079789226 0.480436261 0.0798376700 -0.021212443 0.0051603122
## 1109 -0.735715291 -0.212395608 1.3355307225 -0.424778409 1.0576656796
## 1110 -0.199651979 0.347566967 0.8592741220 2.243881276 0.0329526309
## 1111 -0.991639897 -0.030630153 1.3269059420 -0.394623586 -1.5675014150
## 1112 3.235116452 -0.584063758 -0.5470427886 -0.746768511 -0.4339452252
## 1113 -0.393833619 0.529679776 0.6611636306 -0.730297626 0.3020758634
## 1114 -0.678150632 0.868902231 0.4614963081 0.051808500 1.0437733785
## 1115 -0.409544586 2.369024218 0.3710657724 1.392041248 0.4441439700
## 1116 -0.946583598 0.309443148 -2.4707851040 0.383669604 -1.7318226758
## 1117 4.435142427 -0.383428238 -0.4563051278 1.727107609 -0.3404952715
## 1118 -1.013321991 2.169753619 -1.5581983320 -1.046384693 -0.5500303640
## 1119 -1.132964942 -0.667303818 -0.5716794221 -1.093889016 -1.7318328379
## 1120 0.684619340 -0.669899540 0.7398313242 0.700884606 0.1143426801
## 1121 -0.423102995 -0.076123476 1.6466496396 0.322006538 -0.7370373068
## 1122 -0.701543376 1.462214170 0.0372887041 -1.169615226 -0.7190694138
## 1123 -0.138249460 -1.386534294 1.3408319500 -0.377814766 -0.3266120686
## 1124 -0.286109962 0.483811237 0.0977883846 -0.069347640 -1.7628418055
## 1125 0.316905508 -0.158854609 0.0313360046 -0.487354563 1.0549197294
## 1126 0.112302716 -1.618980074 0.3018035032 -1.878923854 -1.3698646037
## 1127 1.084911031 1.118395583 -0.0542052160 -0.421574255 0.4022005560
## 1128 -1.177187707 -0.580475724 0.1354191524 -0.039293006 0.9729563710
## 1129 -0.576115508 0.819285001 1.3825944421 0.031649255 -1.6759496574
## 1130 0.698329717 1.356954003 -0.7004398243 -0.909835688 1.6073228758
## 1131 -0.027778487 -0.561785428 -0.8094476645 2.421847064 -0.7032445612
## 1132 -0.071210588 -0.143990292 -0.8210032004 0.595188160 0.8334712826
## 1133 -0.174199165 -0.509894058 1.3097419427 0.872720005 1.3081778963
## 1134 -0.147484938 0.814961485 0.7029232006 1.928993470 1.2707463802
## 1135 -0.819982486 -0.625878410 -1.6136851055 -0.237642933 0.3775837011
## 1136 2.819466242 0.010717155 -0.4703495715 0.712289321 1.0052811445
## 1137 -1.052468566 -0.518182866 0.7966474649 1.730605475 0.1291363484
## 1138 -0.985493774 -1.141387894 -0.7809249493 2.082247815 -0.5348293445
## 1139 2.847096429 0.042411283 0.1738460792 1.317705912 -1.1621330376
## 1140 -0.762844363 0.317533389 -0.5659417232 -0.846539399 -0.9428697296
## 1141 2.815009707 -0.928161807 -1.5158168370 -0.086219758 -0.7635358624
## 1142 -0.722799443 -0.413749784 -0.1987824325 0.426803086 -0.6935073942
## 1143 0.453652558 0.634659991 1.3873792769 0.184720296 -0.2156514702
## 1144 0.336473189 -0.110112921 1.3675276674 2.224798958 -1.5297068901
## 1145 -0.774143094 1.493027001 1.4074878992 -0.464121414 1.1106973211
## 1146 -0.878140561 2.066219669 0.0674684754 -0.052580470 0.2960237127
## 1147 0.081696858 -0.420662959 -0.5301490195 -0.173319272 -0.1712069658
## 1148 0.217773861 0.534132546 0.4226486698 2.732459830 0.1162485998
## 1149 -0.087701415 0.820446993 1.4330250264 0.641460311 -1.0618328700
## 1150 -0.459095273 -0.713471362 1.4764012997 1.529517097 1.0123039458
## 1151 0.600069380 0.008852374 1.5311415237 1.622043128 -1.1708449874
## 1152 -0.554797718 -0.637441729 0.5428407350 2.844837332 -0.6860779400
## 1153 -1.050564649 -1.694889864 -0.5993702466 -1.009767600 0.4273147850
## 1154 -1.411821244 -1.482085388 0.3918218204 -1.647376330 -0.7621140707
## 1155 1.461819595 0.868026119 0.0859323942 1.579125271 0.9942484860
## 1156 0.173668382 -1.168011828 -0.0122276381 -0.768699672 0.2618771475
## 1157 1.500140818 -0.758570121 0.1044780939 0.532295412 -1.6619216137
## 1158 0.426871203 -0.493295623 0.1333113537 -0.066381688 -0.1550423233
## 1159 -0.359232351 0.293125041 -0.8795747549 1.326982760 0.3128468501
## 1160 0.089205789 -0.351185439 -1.8612025401 0.336055488 -1.5331507733
## 1161 0.619603383 -0.807908849 -0.7167165499 -1.192987064 1.1916814454
## 1162 0.086595285 -0.374878550 0.9187301596 -1.543039679 1.2359278118
## 1163 0.397582468 1.455249765 1.3993412924 0.253654382 1.4284484407
## 1164 -0.236706033 -0.080270984 -1.1777931975 1.232895548 -0.5736881394
## 1165 -0.195942404 1.096903946 -1.5748583938 0.598143001 0.4413603623
## 1166 0.335023234 1.142496829 -0.6011545769 -1.213031612 -1.9501076737
## 1167 0.853866344 1.107392945 -0.6287663547 -0.929389006 -0.1967404555
## 1168 -0.789487509 0.685074185 -1.5950846416 0.369556934 -1.1265931777
## 1169 -0.603758989 -1.675502510 -0.6156729958 -1.343391349 -1.3318427061
## 1170 -1.167164892 0.894855900 0.0878633177 -0.493819046 -0.5206165075
## 1171 -0.882443758 -0.434624640 -1.5151949155 -0.667212472 1.0252912798
## 1172 -0.835325668 0.846911555 -0.5813790358 1.061655332 -1.2885036496
## 1173 -0.809187609 1.374741468 0.0867539010 -0.339918560 0.4648981595
## 1174 -0.384864725 1.064630299 1.3825302735 -0.113773336 -0.7422882314
## 1175 -0.341632107 -1.670265404 0.0439102913 -1.014147855 1.3462078867
## 1176 -0.283822229 0.504606372 0.6867289983 0.354842308 1.1948019426
## 1177 1.022131923 1.175572794 0.7012180647 1.377485196 -1.5993588923
## 1178 1.464912984 1.661564069 1.4079699608 1.302927657 0.8978661315
## 1179 -1.176071956 -0.882457735 0.1376159895 -0.879878548 0.0258363231
## 1180 0.237298231 -0.676490928 0.7329230125 -0.433835195 0.9860541828
## 1181 -0.719920148 0.016214474 0.6868398795 -0.143202824 -1.5627164221
## 1182 1.836593939 -0.801379401 -0.0833635242 -0.667675034 0.6430065398
## 1183 -0.377269882 -0.256502837 0.0606314477 -0.858263087 0.7291632457
## 1184 -0.402724879 0.685050839 1.2958621716 -0.511218544 1.5266312571
## 1185 1.832848729 1.339177615 0.0736698661 1.255984261 -0.9727763157
## 1186 1.985906235 -0.862664800 0.0402447213 0.386652214 0.3690019053
## 1187 0.244734812 -0.158093644 0.4168749881 -0.486055156 0.7183519181
## 1188 0.268408184 0.560728294 0.3139697385 -1.890025367 1.1266283131
## 1189 -0.245106676 -0.564788273 -0.1764266804 0.212458117 -1.5916283497
## 1190 -0.122463640 -0.332434234 -0.5578909170 -1.040942670 0.7123745324
## 1191 -0.005695705 -0.755235377 -0.2055564430 -0.030425704 1.0178806789
## 1192 0.099014452 -0.482278826 -0.5179814796 -0.743614536 -1.9505090555
## 1193 -0.597733485 1.225396689 0.3135040162 1.528940139 1.3802291708
## 1194 -0.513343482 -0.253387931 0.6616560165 -0.582773588 1.0320749989
## 1195 0.637839257 1.942762103 0.6399183008 -0.859592260 -0.5988557380
## 1196 1.246656623 0.777652990 -0.0504601480 -1.179310147 0.3438342053
## 1197 -0.171282288 -0.045334079 0.0015386266 1.166311903 1.3633756002
## 1198 -1.228542370 -1.470532332 1.3939545595 0.256864329 1.4163546490
## 1199 -0.121337931 -0.711207982 -0.5555028347 0.348641268 0.0597804779
## 1200 -0.720081687 1.486171935 -0.8247282534 2.001518731 -1.5103673356
## 1201 -0.530088251 0.657785603 -0.7210712525 -1.398688249 0.2676537739
## 1202 -0.675774685 -1.684347111 0.0674888906 -0.378863423 1.3453762377
## 1203 -1.139040089 1.154241020 -1.0099571035 -0.514850323 1.6058088542
## 1204 0.357842610 1.001332299 -0.6591724257 1.144355093 -0.8040177445
## 1205 0.235675821 -0.335188682 -0.0811993210 -0.411232693 1.2937542153
## 1206 -1.055550836 0.020076408 0.7347799216 -0.508168920 0.7943438714
## 1207 -0.520116170 -1.034016716 -0.5298269996 -0.554270147 0.8781088667
## 1208 -0.136734813 1.439580542 0.5783920981 1.315119536 -1.2949391778
## 1209 0.572012439 -1.534211375 0.3412176910 -1.331752622 -0.7362414617
## 1210 0.742958127 1.284371914 0.1549389794 -1.848424446 0.0405491900
## 1211 0.129491396 -0.852968329 0.8015554888 1.506094122 -0.7877142576
## 1212 0.290857319 0.041628382 -1.5303300831 -0.717236028 -0.0488941383
## 1213 -0.001565408 -0.839605085 -0.5429867442 0.704674350 -0.8377737309
## 1214 -0.993777009 -0.939381127 -0.5246819720 -0.606048725 0.0016755368
## 1215 0.599080546 -0.338998387 -0.6726564118 -1.160755855 0.1090490211
## 1216 -0.120324163 -0.539904894 0.3671851894 -1.558556401 -2.0386268400
## 1217 0.750702731 -0.494727700 -0.6554774800 -1.120858543 0.9717786634
## 1218 -0.633600836 -0.875457028 0.1445916206 -0.121343968 0.0441288360
## 1219 0.784723593 -0.465052684 0.0336669147 -0.431700361 1.0063353889
## 1220 -1.075789231 1.690964266 0.1188739963 -0.314226418 1.1175989106
## 1221 0.249128583 0.180929481 -1.5066168955 -0.580970653 -0.0070517106
## 1222 1.931766175 -0.876270760 -0.9893593774 -0.649252882 0.6983947242
## 1223 -1.186047466 -1.538581218 0.0814953760 1.101106093 1.3731940852
## 1224 1.895418044 1.120151548 -1.8513656171 0.695520822 0.5679058024
## 1225 -0.837824174 -0.585349673 1.1283867672 0.351508654 0.6447709777
## 1226 2.544926295 -1.066752080 0.7519771999 2.137850028 1.2695088876
## 1227 -0.883553378 0.921380326 -0.8803753641 0.240888848 -1.3453386860
## 1228 -0.468787002 -0.368130166 1.0508855456 -1.289435407 -1.1008696453
## 1229 -0.432245282 1.244524082 0.6325461804 -0.627676891 0.4319820012
## 1230 -0.436056910 0.019344123 1.2730699688 0.099430047 -0.3787723004
## 1231 -0.581513653 -1.643132966 2.3895514824 1.888433227 -0.4004158124
## 1232 0.235857986 1.461060519 0.6904367788 0.488717291 0.2145694329
## 1233 0.097796931 -0.007534367 0.1673481194 1.860467426 0.8287145796
## 1234 -0.199809433 -1.551408443 -1.5485160591 0.700939670 -0.3495101698
## 1235 -0.771356791 2.492613709 -1.2866256971 0.173218689 0.4668068502
## 1236 0.814608076 0.602142013 -1.6294381411 -0.792577864 0.3461077782
## 1237 -0.697629260 1.695876130 1.4372458195 0.797321400 -0.9043606130
## 1238 -0.967816814 0.758882906 0.6394952651 -1.099176697 -1.1459732044
## 1239 -1.129670885 -1.130238757 -1.1899390943 0.408831759 0.6746236455
## 1240 -0.367658358 -1.118499625 -1.5486717761 1.492613529 1.4987811932
## 1241 0.410198911 -0.603474690 -0.6343598548 -1.221789922 0.9490912892
## 1242 -0.202346529 0.270623589 -1.7765465843 1.808224322 1.2577153481
## 1243 2.527587752 -0.190017475 -0.1337977012 0.493673232 -0.8690306820
## 1244 0.414548031 0.547487636 0.9111576725 -1.323583006 0.2379026809
## 1245 -0.091939338 -0.520829216 1.4533345330 -0.153697092 0.7455814310
## 1246 -1.030676599 -1.060352006 -0.5261512607 -0.296756096 -1.7907239499
## 1247 -1.071056295 0.717234147 -1.5339412997 -0.200000721 0.3608501001
## 1248 -0.084151977 -0.513075023 0.0837183469 -0.629414321 -1.6633666590
## 1249 -0.580110526 -0.755295432 -1.4834423532 0.003191177 0.0963326616
## 1250 -0.950790547 -0.442603027 0.7454624146 0.111574643 -0.7585059816
## 1251 -0.801149749 1.036537934 1.0002643713 -1.753109828 1.2165477912
## 1252 -0.151306865 -0.647407410 1.4020453561 0.926509871 0.4215872817
## 1253 -0.362437768 -0.531106075 -0.5726394697 -0.990752292 0.6661464254
## 1254 -0.310526465 1.254950465 -0.2303753268 -0.319203162 1.4000466609
## 1255 0.165491746 0.604555907 0.2773400054 -0.659223863 0.8248219976
## 1256 -0.623271114 0.367123358 0.4482669829 1.490296330 -1.4116129986
## 1257 -0.607193078 0.261736411 -0.3264272449 -0.300548475 0.5872844664
## 1258 -0.480717334 0.250039283 0.1388451614 0.561023340 -1.8031617474
## 1259 -1.115110930 -0.354695892 1.3831250194 -0.114033341 1.0350026595
## 1260 -0.300519658 -0.243774792 0.1237122176 0.555224811 0.1729714466
## 1261 -0.516336026 0.090821523 0.7681367408 -0.223808118 -0.9361618794
## 1262 -0.475568765 0.229190100 -0.6160357905 0.411152860 -0.6663288726
## 1263 -1.027179508 2.002127223 -0.0262893675 0.388517467 0.5569209940
## 1264 -0.780214360 1.854825719 -0.3022656935 0.666263377 -0.2768198481
## 1265 0.871369371 2.554781826 1.1863053405 -0.783480182 0.6940607447
## 1266 -0.497196523 0.545065379 -0.2279126150 0.009776879 1.2593125278
## 1267 -0.407607537 0.296143852 1.3617435149 0.511906615 -0.0064859949
## 1268 0.493498933 -0.982617891 0.1114364577 0.091461177 0.9290805991
## 1269 0.603846444 1.716563754 -1.0152205975 -0.672998423 -1.5065784542
## 1270 0.277583915 -0.674445278 -0.6677660855 -1.096409025 -0.8419068936
## 1271 -0.598593045 0.167646900 -0.6726628042 -1.305535942 1.3642890044
## 1272 -1.280954850 -1.421143790 0.7161249134 -0.279099351 -0.3693912335
## 1273 -0.250235707 -0.771130176 -0.0170804342 -0.515796996 1.2114506182
## 1274 -1.302155850 -1.321227628 1.3691840609 0.121283314 0.5524381682
## 1275 0.311014347 -0.640545336 -0.4334056625 1.840525406 -1.9420770925
## 1276 0.675241849 0.635190777 -0.0859677300 -0.966750577 -1.4746978261
## 1277 -0.310346349 -0.641156721 0.6573854624 0.031998784 -0.5083612464
## 1278 0.893934150 1.992344876 -0.6665487209 -1.456758501 0.2612810755
## 1279 0.272879341 1.003304561 1.3889834035 0.337512542 1.3356928580
## 1280 -0.342693539 -0.250762992 -0.3722490874 -0.305011490 0.4792930920
## 1281 -0.020555162 -0.466549687 -0.2727038445 0.441895148 0.4751126371
## 1282 0.338474734 -0.839980677 -0.5183705895 1.555508159 0.0612882039
## 1283 -0.433071487 1.058890341 1.4303369624 0.277928923 1.0466809627
## 1284 -0.631026149 -0.990637103 0.3705906687 -1.720283387 -0.0677123262
## 1285 0.272038586 0.581123684 -0.0552917995 -0.519830669 0.8840310028
## 1286 -0.301038060 1.592630481 0.6140775194 1.512285602 -0.0794398031
## 1287 -0.671124611 0.529242925 0.3088372680 -0.056679879 0.6493465722
## 1288 -0.799719778 1.416328937 0.3525346105 1.091746277 -0.3498716225
## 1289 -0.036012659 -0.713933787 -0.6552834198 -1.291071916 -0.5575720173
## 1290 -0.203548250 0.582175054 0.6771042561 -0.736609064 -1.4422274816
## 1291 -0.397196299 0.883530262 0.4780987977 0.903872821 1.0602033501
## 1292 -0.057642747 0.240794165 -0.4685582081 1.649081703 0.9966207144
## 1293 -0.441182163 -0.088258441 -0.6131352314 0.706463649 0.1602391682
## 1294 -0.690663698 0.882707164 -0.9749681876 0.191606645 -1.3748789622
## 1295 -0.378556876 0.830262740 -1.2463111379 0.547609804 -0.4245454049
## 1296 2.027824683 -2.086828019 0.9475564241 -1.192604965 0.3722419816
## 1297 -0.283940092 1.422475604 0.0941623992 -0.395633191 -1.2833193763
## 1298 -0.728769561 -1.412013743 0.7793217576 1.314640125 1.1397627131
## 1299 0.711741653 0.054539594 1.5899313498 0.740567789 1.3660352979
## 1300 -0.084989365 0.410986479 -0.6693475293 -1.395709618 0.2413591158
## 1301 0.308559602 -1.042898398 0.0474263180 -0.320143656 -0.5800499351
## 1302 2.144928430 1.063549738 -0.3711185047 -0.276094144 -0.3985801666
## 1303 -0.320520889 -0.551481316 1.0872293942 0.997260970 -1.1134873707
## 1304 1.598214918 1.194518241 0.6687593096 -0.570347730 0.4825733803
## 1305 -0.130127142 0.104603092 1.3476869604 0.686659573 -0.6269329530
## 1306 0.495846394 1.311533253 -1.6556699330 -0.154543810 1.0606903940
## 1307 -0.279589863 0.409562258 1.4373293452 0.147434985 -1.7384851179
## 1308 -0.860637767 -0.421603628 1.3925231413 -0.448726764 0.1440324149
## 1309 -0.315103697 0.420429307 -1.5565883120 -0.654022608 -0.8757872306
## 1310 -0.497730192 -0.907517009 -0.5250123005 -0.289990208 0.0187459574
## 1311 1.163477746 1.240489472 -0.0564736304 0.375390452 -1.6332643845
## 1312 -1.671192990 -0.556452936 -1.7121871218 1.353594987 -0.6840674032
## 1313 -0.898711369 0.162225894 1.4983824233 1.588001943 0.5803212018
## 1314 -1.224310338 0.452561188 1.4047120331 0.677837833 -1.4515024535
## 1315 0.215650242 0.759726991 0.9483578256 -1.383839438 -0.0083623896
## 1316 -0.576449868 0.979792650 0.7061840398 -0.674161442 0.9798545274
## 1317 0.231471551 0.088425980 -0.6346383724 -1.103884221 -1.8704430608
## 1318 -0.688365595 -1.372814500 -1.5365354371 -0.346281421 1.1406134004
## 1319 0.136990178 -2.027773935 0.3715087328 0.194903515 1.2377127402
## 1320 -1.060812668 1.498944597 0.3719059192 -0.990652090 0.9958126669
## 1321 -0.331494589 0.762787861 -0.9044138625 0.489997213 0.0997918895
## 1322 -0.595978606 1.239823941 -0.0241580164 -0.198307303 -0.7683061963
## 1323 0.642763877 -0.029997185 -1.6746213888 -0.815244597 1.3903350579
## 1324 -0.803752723 -1.107243695 -0.6230966309 -1.343326719 0.2418699953
## 1325 -0.467613589 0.205090869 0.0788104010 1.588924997 1.7317283817
## 1326 -0.699016687 0.724932329 -0.0315291872 -0.381166582 1.1903531859
## 1327 -0.604217033 1.785200865 -0.2072858273 -0.334157553 0.3115328228
## 1328 1.863672464 -0.063479609 1.3416004059 -0.266029157 -1.5084605397
## 1329 -0.268546943 -1.691891500 0.0979170022 1.220211910 -0.3980626269
## 1330 -0.987804942 -1.197341784 0.6516635993 -0.352975406 1.4312900641
## 1331 1.911067929 1.076939867 0.0449025550 -0.757366431 -1.3229692445
## 1332 2.787410644 0.218340047 0.7136309526 0.167007680 1.2071678401
## 1333 -0.978759016 -0.929450680 -1.5121792465 1.607873602 1.2342389985
## 1334 0.295350522 0.941810651 0.6384772439 0.085967202 0.3946165816
## 1335 -0.414506934 -0.791397357 0.5226455050 1.622956420 1.0454804054
## 1336 -0.806462175 1.794851302 -0.5936948323 0.478211205 1.1120140570
## 1337 -0.174369883 2.190748676 0.1802845176 -1.845430523 -0.6685711604
## 1338 -1.067486608 -0.416970105 0.7302869137 -0.538903406 -0.7634753482
## 1339 -1.148426529 -0.420771087 -1.5313484634 0.061272155 -0.7475698134
## 1340 -1.233596588 -1.454901735 0.7093835780 -0.237084952 1.3918281030
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## 1342 -0.016118767 -0.837788756 0.1442714877 1.075034538 -0.8114871971
## 1343 0.159782501 -0.305228716 -0.5992124014 -1.019285492 0.1235182312
## 1344 -1.064598354 0.065959591 1.3948842616 0.148070905 1.1242365870
## 1345 -0.561833293 1.170354440 1.3798237998 0.151105283 1.0478450112
## 1346 -0.373531215 -0.970363929 0.6928433017 0.838738433 1.2052726102
## 1347 0.540536221 -0.861227934 -1.5920649170 1.741649936 -0.5079609424
## 1348 0.056750090 -1.285134489 -1.6380054381 -0.809733114 -0.3232647504
## 1349 2.013115732 0.123366021 1.4314458211 -0.416931993 -1.7473654229
## 1350 -1.149068150 -0.792545959 -0.9042879239 -0.622356318 -0.5164291639
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## 1352 2.721244943 -0.301173311 -0.5659450422 0.966597193 1.0833669506
## 1353 -0.395922929 0.869268711 1.3020319001 -0.455466459 -0.8021005773
## 1354 -0.590409380 -0.011040050 1.4400534028 1.286924370 0.8378661771
## 1355 0.139420929 -0.144463380 -0.7689526104 1.059803137 -1.3456314837
## 1356 -0.473712133 -0.100419155 -1.2044954658 1.826907482 0.5924560655
## 1357 -0.393164373 0.873709374 0.6523699015 -0.126198626 0.3703322556
## 1358 0.953398456 1.614360854 2.2830199190 -0.714695591 0.5138497701
## 1359 -0.214935993 -0.824635813 -0.6042729330 -0.436687012 0.3166165603
## 1360 -0.183456679 -0.624500126 -1.6399573692 -0.826897973 1.5621348728
## 1361 -1.242703332 1.551343552 -0.9092952289 -0.508703594 -1.2423134666
## 1362 -0.483634223 -1.254847152 -0.5307649550 -0.642952566 -0.0492937967
## 1363 -0.190300939 1.131808464 -0.0179044970 -1.061282253 -0.7846906593
## 1364 0.069562708 -0.193974533 -0.8052379033 0.569517031 -0.9367707958
## 1365 -0.074093593 -1.246569055 -0.5969048103 -1.341595098 0.2356904185
## 1366 -1.192830336 -0.389040643 1.4434476399 2.012174208 0.1687350096
## 1367 -0.525189061 1.450006107 0.0823295770 0.972610002 -1.5784729855
## 1368 -0.906258650 -0.093886054 -0.1541534652 -0.027136486 -0.9243292453
## 1369 0.704376641 -0.705458381 -0.4642330643 1.155548867 -0.1879915228
## 1370 -0.326002655 -0.461857745 0.0786321311 0.085459208 1.2919933798
## 1371 0.048695428 1.931911837 1.6165005164 0.011760425 0.2448191961
## 1372 -0.228664786 2.175644209 1.2674554690 0.633710936 0.9211625521
## 1373 0.198435667 -0.638043766 1.3218699562 0.318406720 -1.3582936606
## 1374 0.807608522 -0.957101308 0.7483556284 0.206570270 0.9578748799
## 1375 1.203857219 1.383912665 -1.6851033945 1.104095654 1.3736161461
## 1376 -0.814896500 -0.333295166 0.0114562622 -0.754775588 -1.3596899944
## 1377 -0.117816209 -0.711627453 0.2782104145 -1.043622616 -0.6113020004
## 1378 1.457200168 -0.133998699 -0.7888148514 -1.560263419 -0.1627017534
## 1379 -0.522393026 0.797916045 -0.6316422829 -0.149115833 -0.8613538951
## 1380 -1.079884065 -0.476467009 0.7975982235 1.472686955 -1.6328011474
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## 1382 -0.787496282 -0.607602787 -0.8155303839 1.130848732 0.1469017648
## 1383 -0.650444971 -0.898025670 2.2831523103 -0.800259594 0.2888174540
## 1384 -0.503096351 0.085115759 0.7431662557 0.199383576 -1.8273056547
## 1385 0.872128518 -0.706355689 -1.5141322229 -0.773904047 -1.6442900789
## 1386 0.275518500 -0.125915781 -0.8036377131 0.886053136 0.8471949959
## 1387 -0.672428242 -0.765371894 0.4811712980 0.122457757 0.1450124374
## 1388 -0.543834788 -0.484695144 0.4528450865 0.039476327 -1.5767291483
## 1389 -0.355473156 0.708796313 -0.5236953835 0.156030019 0.0407393925
## 1390 -0.029058707 -0.635818967 1.4026590197 -0.379065879 1.0094740968
## 1391 -1.038817244 0.361601866 -1.4861215154 0.801014175 0.3086645293
## 1392 -1.077642755 1.021942613 0.3467534942 -0.138117772 -1.3213638081
## 1393 0.236474864 -0.414601649 -0.5422216139 -0.489884686 -0.1712039104
## 1394 -0.338637736 -0.992383640 -0.5280031778 -0.354192236 0.8901476697
## 1395 -0.579877431 1.672063589 -0.5743094931 -1.069865790 1.0856744802
## 1396 0.152222927 -0.544912020 -0.4511287173 1.500376233 -1.9341508629
## 1397 0.114403539 2.392175371 0.3568506803 2.263655945 -1.3190793805
## 1398 -0.158832526 0.612398019 -1.0943276670 0.137937417 -1.1497667209
## 1399 0.148952222 -1.107679837 0.0476630685 -0.387123967 1.1720809407
## 1400 0.635798543 -0.319148789 0.0274798544 0.053852506 -1.6186879246
## 1401 -0.242042253 -0.219958913 0.7122068457 -0.549783822 0.7595634850
## 1402 2.002521745 1.337389850 0.6977675459 1.829873478 0.2231311415
## 1403 -1.003494900 -1.332341078 -0.6957015740 -1.311196483 1.3575948361
## 1404 1.895515445 -0.573947415 1.4872959642 1.216766464 -0.9770870099
## 1405 1.220859999 -1.314376193 0.0706769916 1.429116580 1.1758246552
## 1406 0.618144838 -0.221175383 1.0691837257 -0.625913580 0.1390774359
## 1407 -0.088120260 1.696929608 1.2106488813 0.308550241 0.5313626746
## 1408 -0.798598246 -0.979802216 -0.8719617786 -0.607455236 -0.5367860314
## 1409 -0.682694673 -1.602844841 0.4062048568 -0.612049266 1.0081231085
## 1410 0.558773869 -0.700762003 0.9967110930 -0.360227244 0.9128078098
## 1411 0.295383114 -0.241257596 0.6342404775 -0.754221417 -0.4244302824
## 1412 -1.301129148 0.169444885 0.7451322444 -0.723677149 0.2353728419
## 1413 -0.036069050 -1.077012972 -0.2278671084 -0.220254360 1.2496298839
## 1414 -1.247326313 -0.015067150 -0.9413711664 -0.753799794 1.6909888830
## 1415 1.419878921 -0.250194510 0.0695416033 1.562654122 -1.5677070266
## 1416 -1.021639246 -0.547601716 -0.9616104581 -0.620800417 -0.4802475579
## 1417 0.649752690 -0.593196928 0.7538563602 -0.480198557 0.7204789160
## 1418 -0.780983991 -1.043223360 0.0119852913 -0.982326996 -1.5010446692
## 1419 0.030395129 0.211835569 0.0755235909 -0.426937261 -1.8147247347
## 1420 -0.496378152 1.788315264 0.4245699741 1.754040056 1.2233838479
## 1421 -0.333902927 0.126699460 -0.6815699479 -1.306152190 1.0646968691
## 1422 1.329506355 -0.875861085 -1.3240690428 0.123669317 0.7373989381
## 1423 -1.049991167 1.511082599 0.0705037710 -0.053131908 1.0694118695
## 1424 -0.818266688 -1.669100876 1.0330022109 -1.501456307 0.9960764013
## 1425 0.166745637 -0.284205190 0.1206769833 -0.024335299 -1.0099392420
## 1426 0.127722175 -1.433017050 -0.5855102435 0.203326375 -0.6683043380
## 1427 -0.466067658 -0.230227650 0.8440748671 2.391202582 -0.0830130376
## 1428 -1.165536432 2.181318622 -1.6143545750 -1.016970229 -1.4480597758
## 1429 -0.867248658 -0.202486671 0.7392970045 -0.615911483 -1.0131667699
## 1430 -0.336592155 0.304234339 -0.6779526017 0.770012195 -0.9445254797
## 1431 1.594207673 -0.312855580 0.1051566529 -0.080327459 -0.6930160820
## 1432 0.966525516 -0.635413791 -0.5089458998 -1.136109664 -0.1952063552
## 1433 1.628867411 -0.912140628 -0.5449114852 -0.275757415 0.0559157211
## 1434 -0.602222403 -1.229192368 -0.8504786015 0.164713858 -1.4563811096
## 1435 0.384109584 0.648449789 -1.5652828560 2.261172828 -1.6856538516
## 1436 -0.571522947 1.116204399 -0.7211940078 -1.471938920 -0.5258170706
## 1437 -1.256712127 -1.390961219 1.3718087767 -0.189338854 0.5396549995
## 1438 1.280412970 0.019188740 -1.5420898195 -0.052488424 1.1421214695
## 1439 -1.395844572 -0.425994502 0.4999143356 0.916943973 1.0865533495
## 1440 0.438111521 -0.864092722 -0.6010704859 -1.038282089 -1.7452617713
## 1441 -0.662011521 0.866245900 0.6302903157 -0.709061318 1.5369328384
## 1442 1.109563242 0.505372842 -0.9999705967 -0.372094083 0.0512545151
## 1443 -1.103195273 1.693937879 0.3704194937 -2.033559090 -1.6230772199
## 1444 2.369229469 0.439769879 -0.8749142645 -0.559738575 -1.3768805846
## 1445 0.032592871 1.778828381 -2.0508428483 0.338703109 1.7878190589
## 1446 2.030759043 -0.608733942 0.8547906265 2.310945922 -1.8717001180
## 1447 0.201097943 -0.717671825 0.1445396772 1.929611111 0.9854412630
## 1448 0.663766634 -0.486615008 -1.4478907436 0.917256892 0.7772914411
## 1449 0.209243160 0.150257162 0.6558296526 -0.583064295 0.2358960174
## 1450 -0.743728136 -0.366209395 1.3666407353 -0.306037252 1.0367480286
## 1451 0.536285859 -0.401850049 -0.4782803927 1.501937103 -0.1402835692
## 1452 0.323489799 -0.985159957 -0.6394443197 -0.389657019 -1.4772204077
## 1453 0.081387134 2.009806578 -0.0552000534 -1.174467869 -0.6169262975
## 1454 -0.191140729 0.760747843 -1.5071690913 0.240486118 -0.7890388822
## 1455 -0.317048006 1.620780822 -0.0062670552 0.782766719 1.3884204407
## 1456 -0.621595124 0.464830106 0.0174916580 -0.848629437 -0.0291864731
## 1457 0.333062697 -0.503390924 1.0970405596 0.465082392 -0.2054268299
## 1458 -0.447836979 0.330576263 0.0285286543 -0.814616048 -0.0463616270
## 1459 -0.490040292 -0.157186497 -0.5917799674 -1.167185762 -0.1537424921
## 1460 -0.789663284 -0.194750796 0.7209362379 0.384404110 1.3557950095
## 1461 -0.729739877 0.108420797 -0.3706488993 3.538777915 0.9884322841
## 1462 0.404976050 1.083014074 1.3118651629 2.262386882 1.3342585747
## 1463 1.865987905 -1.866527036 -1.5282088616 1.600847174 -0.3606740275
## 1464 0.389452105 -0.757228139 1.4234180344 -0.004402066 -0.7714978440
## 1465 -0.723267174 -1.051409469 0.1125859930 -0.488644290 0.8822654175
## 1466 -0.537973485 -0.199149211 -0.6176020137 0.905185783 0.4383741597
## 1467 0.288063247 -0.162302425 1.2624871110 -0.211934095 1.6646342030
## 1468 -0.363648244 -0.644445192 0.7699614858 -0.413237143 -0.7820553802
## 1469 0.392994518 0.371654956 -0.3461808265 -0.121991477 1.2095418303
## 1470 -0.413010977 -0.340161244 1.0000164249 -0.793819984 -0.8079035956
#Clustering
# Kmeans optimal clusters
# As we have two factors, Yes and No in Attrition, we check the clustering for 2 clusters only.
set.seed(42)
matstd_attr <- scale(efa_data)
km.res <- kmeans(matstd_attr, 2, nstart = 10)
fviz_cluster(km.res, data = matstd_attr,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal())
# We have used the efa_data for the clustering of the forst approach.
# We can check the precision and recall using the confusion matrix below.
Clustered <- ifelse(km.res$cluster > 1, "Attrited", "Not Attrited")
Actual <- ifelse(attr$Attrition == 1, "Attrited", "Not Attrited")
confusion_mat <- table(Clustered, Actual)
confusion_mat
## Actual
## Clustered Not Attrited
## Attrited 903
## Not Attrited 567
accuracy <- sum(diag(confusion_mat)) / sum(confusion_mat)
precision <- confusion_mat[1, 1] / sum(confusion_mat[, 1])
recall <- confusion_mat[1, 1] / sum(confusion_mat[1, ])
cat("Accuracy:", round(accuracy, 3), "\n")
## Accuracy: 0.614
cat("Precision:", round(precision, 3), "\n")
## Precision: 0.614
cat("Recall:", round(recall, 3), "\n")
## Recall: 1
# Although we have a recall of 1, we can see that the confusion matrix shows the clustering is done in a way where almost all the employees are on the same side.
# This shows that we cannot classify our data into Yes and No in Attrition based on the variables given.
# We can now check the clustering using the second approach.
#New Data
set.seed(42)
matstd_attr1 <- scale(pca_data)
km.res1 <- kmeans(matstd_attr1, 2, nstart = 10)
fviz_cluster(km.res1, data = matstd_attr1,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal())
# We have used the pca_data for the clustering of the forst approach.
# We can check the precision and recall using the confusion matrix below.
Clustered1 <- ifelse(km.res$cluster > 1, "Attrited", "Not Attrited")
Actual <- ifelse(attr$Attrition == 1, "Attrited", "Not Attrited")
confusion_mat1 <- table(Clustered1, Actual)
confusion_mat1
## Actual
## Clustered1 Not Attrited
## Attrited 903
## Not Attrited 567
accuracy1 <- sum(diag(confusion_mat1)) / sum(confusion_mat1)
precision1 <- confusion_mat1[1, 1] / sum(confusion_mat1[, 1])
recall1 <- confusion_mat1[1, 1] / sum(confusion_mat1[1, ])
cat("Accuracy:", round(accuracy1, 3), "\n")
## Accuracy: 0.614
cat("Precision:", round(precision1, 3), "\n")
## Precision: 0.614
cat("Recall:", round(recall1, 3), "\n")
## Recall: 1
#The precision is obtained to be 39% which is not so good.
#Regression & Logistic Regression
attrition_data <- read.csv("/Users/meet/Desktop/Attrition Data copy.csv",row.names=1, fill = TRUE)
attrition_data
## Department MaritalStatus EducationField Attrition Education
## 1 Sales Single Life Sciences Yes 2
## 2 Research & Development Married Life Sciences No 1
## 3 Research & Development Single Other Yes 2
## 4 Research & Development Married Life Sciences No 4
## 5 Research & Development Married Medical No 1
## 6 Research & Development Single Life Sciences No 2
## 7 Research & Development Married Medical No 3
## 8 Research & Development Divorced Life Sciences No 1
## 9 Research & Development Single Life Sciences No 3
## 10 Research & Development Married Medical No 3
## 11 Research & Development Married Medical No 3
## 12 Research & Development Single Life Sciences No 2
## 13 Research & Development Divorced Life Sciences No 1
## 14 Research & Development Divorced Medical No 2
## 15 Research & Development Single Life Sciences Yes 3
## 16 Research & Development Divorced Life Sciences No 4
## 17 Research & Development Divorced Life Sciences No 2
## 18 Research & Development Divorced Medical No 2
## 19 Sales Married Life Sciences No 4
## 20 Research & Development Single Life Sciences No 3
## 21 Research & Development Divorced Other No 2
## 22 Sales Single Life Sciences Yes 4
## 23 Research & Development Single Life Sciences No 4
## 24 Research & Development Single Life Sciences No 2
## 25 Research & Development Single Medical Yes 1
## 26 Research & Development Divorced Other No 3
## 27 Research & Development Single Life Sciences Yes 1
## 28 Sales Married Marketing No 4
## 29 Research & Development Married Medical No 4
## 30 Sales Single Marketing No 4
## 31 Research & Development Single Medical No 3
## 32 Research & Development Married Other No 4
## 33 Research & Development Single Medical No 2
## 34 Sales Married Technical Degree Yes 3
## 35 Research & Development Married Medical Yes 3
## 36 Research & Development Divorced Medical No 2
## 37 Sales Married Marketing Yes 2
## 38 Sales Married Marketing No 3
## 39 Research & Development Married Life Sciences No 4
## 40 Sales Married Life Sciences No 3
## 41 Research & Development Divorced Other No 2
## 42 Research & Development Divorced Life Sciences No 4
## 43 Research & Development Single Life Sciences Yes 3
## 44 Sales Single Life Sciences No 3
## 45 Research & Development Single Medical No 2
## 46 Research & Development Married Technical Degree Yes 3
## 47 Sales Single Marketing No 4
## 48 Research & Development Married Life Sciences No 2
## 49 Sales Single Marketing No 4
## 50 Research & Development Married Life Sciences No 1
## 51 Research & Development Single Life Sciences Yes 2
## 52 Research & Development Single Technical Degree Yes 4
## 53 Sales Divorced Marketing No 5
## 54 Research & Development Married Medical No 2
## 55 Sales Married Marketing No 3
## 56 Research & Development Single Life Sciences No 2
## 57 Sales Married Life Sciences No 5
## 58 Research & Development Married Medical No 4
## 59 Research & Development Divorced Life Sciences No 4
## 60 Research & Development Divorced Life Sciences No 4
## 61 Research & Development Married Medical No 3
## 62 Research & Development Single Life Sciences No 5
## 63 Research & Development Divorced Medical No 2
## 64 Sales Single Life Sciences No 3
## 65 Research & Development Divorced Technical Degree No 3
## 66 Research & Development Divorced Medical No 3
## 67 Research & Development Single Life Sciences No 3
## 68 Research & Development Divorced Life Sciences No 3
## 69 Research & Development Married Medical No 3
## 70 Research & Development Married Medical Yes 3
## 71 Sales Single Life Sciences No 1
## 72 Research & Development Married Life Sciences No 3
## 73 Research & Development Single Medical No 4
## 74 Research & Development Married Life Sciences No 3
## 75 Research & Development Married Life Sciences No 3
## 76 Research & Development Single Life Sciences No 4
## 77 Sales Single Marketing No 4
## 78 Research & Development Married Other No 4
## 79 Research & Development Single Medical No 4
## 80 Human Resources Divorced Medical No 2
## 81 Research & Development Married Life Sciences No 1
## 82 Research & Development Single Medical No 3
## 83 Sales Married Life Sciences No 2
## 84 Research & Development Divorced Medical No 3
## 85 Research & Development Married Medical No 2
## 86 Research & Development Single Life Sciences No 3
## 87 Sales Divorced Technical Degree No 1
## 88 Research & Development Married Life Sciences No 4
## 89 Research & Development Married Life Sciences No 3
## 90 Sales Single Medical Yes 2
## 91 Research & Development Married Life Sciences No 4
## 92 Sales Single Marketing No 4
## 93 Sales Divorced Medical No 2
## 94 Research & Development Married Medical No 3
## 95 Sales Single Medical No 4
## 96 Research & Development Married Technical Degree No 4
## 97 Sales Married Other No 2
## 98 Sales Married Medical No 3
## 99 Sales Single Medical No 4
## 100 Research & Development Married Medical No 3
## 101 Human Resources Divorced Human Resources Yes 4
## 102 Research & Development Single Life Sciences No 1
## 103 Research & Development Single Life Sciences Yes 3
## 104 Research & Development Single Other No 4
## 105 Research & Development Divorced Life Sciences No 2
## 106 Human Resources Married Human Resources No 4
## 107 Research & Development Married Life Sciences No 3
## 108 Sales Single Marketing Yes 3
## 109 Research & Development Married Medical No 1
## 110 Research & Development Single Medical No 3
## 111 Research & Development Single Medical No 4
## 112 Research & Development Single Life Sciences Yes 3
## 113 Human Resources Single Human Resources No 3
## 114 Research & Development Married Life Sciences No 1
## 115 Research & Development Divorced Life Sciences No 4
## 116 Sales Single Life Sciences No 3
## 117 Research & Development Single Medical No 3
## 118 Sales Married Technical Degree No 2
## 119 Research & Development Divorced Life Sciences No 2
## 120 Sales Married Life Sciences No 2
## 121 Research & Development Divorced Life Sciences No 3
## 122 Sales Married Marketing No 2
## 123 Research & Development Married Life Sciences Yes 4
## 124 Research & Development Single Life Sciences No 3
## 125 Sales Married Life Sciences Yes 4
## 126 Research & Development Married Other No 3
## 127 Research & Development Married Medical Yes 4
## 128 Sales Single Marketing Yes 1
## 129 Research & Development Married Technical Degree No 1
## 130 Research & Development Married Medical No 4
## 131 Research & Development Single Medical No 3
## 132 Sales Single Marketing No 3
## 133 Sales Married Life Sciences Yes 3
## 134 Sales Divorced Life Sciences No 1
## 135 Human Resources Married Life Sciences No 1
## 136 Research & Development Divorced Medical No 2
## 137 Research & Development Single Life Sciences Yes 4
## 138 Sales Married Life Sciences No 4
## 139 Sales Married Life Sciences No 3
## 140 Human Resources Married Human Resources No 3
## 141 Research & Development Single Medical Yes 3
## 142 Research & Development Single Medical No 3
## 143 Research & Development Single Technical Degree No 5
## 144 Research & Development Single Life Sciences No 3
## 145 Sales Divorced Medical No 2
## 146 Research & Development Divorced Technical Degree No 3
## 147 Research & Development Single Medical No 1
## 148 Research & Development Divorced Life Sciences No 3
## 149 Research & Development Married Life Sciences No 4
## 150 Research & Development Single Medical No 1
## 151 Research & Development Divorced Medical No 3
## 152 Sales Married Marketing No 5
## 153 Sales Married Marketing No 2
## 154 Research & Development Divorced Life Sciences No 3
## 155 Sales Single Marketing No 3
## 156 Research & Development Married Technical Degree No 1
## 157 Research & Development Married Medical No 4
## 158 Research & Development Married Medical No 3
## 159 Sales Married Marketing No 4
## 160 Sales Married Marketing No 4
## 161 Research & Development Married Medical No 1
## 162 Research & Development Divorced Medical No 3
## 163 Research & Development Married Medical No 3
## 164 Research & Development Divorced Life Sciences No 2
## 165 Research & Development Divorced Medical No 3
## 166 Research & Development Single Life Sciences No 3
## 167 Research & Development Divorced Life Sciences No 3
## 168 Sales Married Life Sciences No 3
## 169 Sales Single Life Sciences No 4
## 170 Research & Development Single Life Sciences No 5
## 171 Research & Development Married Technical Degree No 3
## 172 Sales Single Technical Degree Yes 1
## 173 Research & Development Single Medical No 2
## 174 Research & Development Divorced Medical No 3
## 175 Sales Divorced Life Sciences No 2
## 176 Research & Development Divorced Life Sciences No 3
## 177 Research & Development Single Life Sciences No 3
## 178 Research & Development Single Life Sciences Yes 3
## 179 Sales Divorced Marketing No 2
## 180 Research & Development Single Life Sciences No 2
## 181 Research & Development Married Medical No 1
## 182 Research & Development Single Medical No 2
## 183 Sales Single Marketing Yes 2
## 184 Research & Development Married Medical No 3
## 185 Research & Development Divorced Medical No 2
## 186 Research & Development Married Medical No 3
## 187 Research & Development Married Medical No 1
## 188 Research & Development Single Medical No 4
## 189 Research & Development Married Life Sciences No 1
## 190 Research & Development Single Medical No 3
## 191 Research & Development Married Life Sciences No 4
## 192 Research & Development Single Medical No 3
## 193 Research & Development Married Life Sciences Yes 2
## 194 Research & Development Divorced Medical No 3
## 195 Research & Development Married Medical No 2
## 196 Research & Development Married Life Sciences No 3
## 197 Research & Development Single Medical No 3
## 198 Research & Development Divorced Medical No 2
## 199 Research & Development Married Life Sciences No 4
## 200 Research & Development Married Technical Degree No 3
## 201 Research & Development Married Technical Degree No 1
## 202 Research & Development Divorced Life Sciences No 4
## 203 Research & Development Divorced Medical No 4
## 204 Research & Development Married Medical No 2
## 205 Research & Development Married Medical Yes 1
## 206 Sales Married Marketing Yes 3
## 207 Research & Development Divorced Life Sciences No 3
## 208 Research & Development Single Medical No 1
## 209 Research & Development Married Life Sciences No 5
## 210 Research & Development Divorced Medical No 4
## 211 Sales Married Medical Yes 4
## 212 Research & Development Single Life Sciences No 1
## 213 Sales Single Life Sciences No 3
## 214 Research & Development Married Life Sciences No 4
## 215 Research & Development Single Technical Degree Yes 3
## 216 Sales Single Life Sciences No 3
## 217 Sales Single Marketing Yes 4
## 218 Research & Development Single Technical Degree Yes 3
## 219 Sales Single Medical No 3
## 220 Sales Married Marketing No 3
## 221 Research & Development Single Life Sciences No 2
## 222 Research & Development Married Medical No 4
## 223 Research & Development Divorced Other No 3
## 224 Sales Divorced Life Sciences No 3
## 225 Research & Development Married Medical No 4
## 226 Research & Development Married Life Sciences No 3
## 227 Sales Divorced Marketing No 4
## 228 Sales Married Medical No 1
## 229 Sales Single Marketing No 3
## 230 Research & Development Single Medical Yes 1
## 231 Research & Development Single Life Sciences No 3
## 232 Research & Development Married Technical Degree No 2
## 233 Human Resources Married Medical No 2
## 234 Sales Divorced Medical No 4
## 235 Research & Development Married Medical Yes 3
## 236 Sales Married Marketing No 3
## 237 Research & Development Married Life Sciences Yes 2
## 238 Sales Single Life Sciences No 4
## 239 Sales Married Life Sciences No 2
## 240 Research & Development Single Life Sciences Yes 3
## 241 Research & Development Divorced Medical No 4
## 242 Sales Married Marketing No 4
## 243 Research & Development Divorced Life Sciences No 2
## 244 Research & Development Divorced Technical Degree No 2
## 245 Research & Development Married Other No 3
## 246 Research & Development Divorced Medical No 4
## 247 Research & Development Married Life Sciences No 4
## 248 Research & Development Married Life Sciences No 4
## 249 Research & Development Married Medical No 2
## 250 Research & Development Married Life Sciences No 4
## 251 Research & Development Divorced Medical Yes 3
## 252 Research & Development Single Technical Degree No 4
## 253 Research & Development Single Life Sciences No 3
## 254 Research & Development Single Life Sciences No 2
## 255 Sales Divorced Marketing No 2
## 256 Research & Development Married Life Sciences No 3
## 257 Research & Development Divorced Medical No 3
## 258 Research & Development Divorced Medical No 2
## 259 Research & Development Married Life Sciences No 3
## 260 Research & Development Single Medical Yes 2
## 261 Research & Development Married Life Sciences No 3
## 262 Sales Married Life Sciences No 2
## 263 Research & Development Single Technical Degree No 1
## 264 Sales Married Technical Degree No 3
## 265 Research & Development Single Life Sciences Yes 4
## 266 Sales Married Medical No 3
## 267 Research & Development Married Medical No 3
## 268 Research & Development Divorced Life Sciences No 2
## 269 Research & Development Married Medical No 2
## 270 Research & Development Married Life Sciences No 3
## 271 Research & Development Single Medical No 3
## 272 Research & Development Married Life Sciences Yes 4
## 273 Research & Development Married Medical No 3
## 274 Sales Married Medical No 4
## 275 Research & Development Single Medical No 2
## 276 Research & Development Divorced Medical No 4
## 277 Research & Development Divorced Life Sciences No 3
## 278 Sales Divorced Medical No 2
## 279 Research & Development Divorced Life Sciences No 3
## 280 Research & Development Divorced Life Sciences No 1
## 281 Research & Development Married Medical No 4
## 282 Sales Married Life Sciences No 1
## 283 Sales Single Life Sciences No 2
## 284 Research & Development Married Technical Degree No 2
## 285 Research & Development Married Medical No 2
## 286 Research & Development Single Life Sciences No 3
## 287 Research & Development Divorced Life Sciences Yes 3
## 288 Research & Development Divorced Life Sciences No 4
## 289 Research & Development Divorced Medical Yes 4
## 290 Research & Development Single Life Sciences No 2
## 291 Research & Development Single Life Sciences No 4
## 292 Research & Development Single Technical Degree No 3
## 293 Sales Divorced Marketing No 3
## 294 Sales Single Marketing Yes 4
## 295 Research & Development Married Medical No 3
## 296 Sales Married Marketing No 3
## 297 Research & Development Single Life Sciences Yes 3
## 298 Sales Married Marketing No 3
## 299 Research & Development Married Life Sciences No 4
## 300 Research & Development Divorced Medical No 3
## 301 Sales Single Life Sciences No 4
## 302 Sales Single Medical No 3
## 303 Research & Development Single Medical No 2
## 304 Sales Married Technical Degree No 3
## 305 Research & Development Divorced Medical No 3
## 306 Research & Development Married Life Sciences No 4
## 307 Sales Married Life Sciences No 3
## 308 Research & Development Married Life Sciences No 2
## 309 Research & Development Divorced Life Sciences No 4
## 310 Research & Development Married Technical Degree No 4
## 311 Human Resources Married Human Resources No 3
## 312 Research & Development Divorced Life Sciences No 3
## 313 Research & Development Divorced Life Sciences No 4
## 314 Research & Development Married Life Sciences No 4
## 315 Research & Development Married Medical No 1
## 316 Research & Development Single Life Sciences No 4
## 317 Research & Development Single Technical Degree No 2
## 318 Research & Development Married Medical Yes 4
## 319 Research & Development Single Life Sciences No 3
## 320 Sales Married Technical Degree No 2
## 321 Sales Single Life Sciences No 3
## 322 Sales Divorced Marketing No 3
## 323 Research & Development Single Medical No 4
## 324 Research & Development Married Medical Yes 4
## 325 Research & Development Married Medical No 2
## 326 Research & Development Married Life Sciences No 2
## 327 Research & Development Married Medical No 2
## 328 Sales Married Medical Yes 2
## 329 Sales Single Marketing No 3
## 330 Research & Development Married Life Sciences No 5
## 331 Research & Development Divorced Life Sciences No 4
## 332 Sales Married Marketing No 1
## 333 Research & Development Single Life Sciences No 4
## 334 Research & Development Married Life Sciences No 3
## 335 Research & Development Married Other No 4
## 336 Sales Married Medical No 2
## 337 Research & Development Married Other Yes 4
## 338 Research & Development Single Other No 5
## 339 Sales Divorced Marketing No 3
## 340 Sales Married Marketing No 4
## 341 Research & Development Divorced Medical No 2
## 342 Research & Development Divorced Life Sciences No 2
## 343 Research & Development Single Medical No 4
## 344 Sales Divorced Marketing No 1
## 345 Research & Development Single Technical Degree No 4
## 346 Research & Development Divorced Life Sciences No 1
## 347 Research & Development Single Medical No 3
## 348 Sales Single Medical No 1
## 349 Research & Development Single Life Sciences No 5
## 350 Sales Married Life Sciences No 3
## 351 Human Resources Divorced Technical Degree No 1
## 352 Research & Development Married Medical No 3
## 353 Sales Married Medical No 1
## 354 Research & Development Divorced Medical No 3
## 355 Sales Married Technical Degree No 2
## 356 Sales Married Life Sciences No 3
## 357 Research & Development Single Other No 4
## 358 Sales Single Technical Degree Yes 1
## 359 Sales Single Medical No 5
## 360 Sales Married Medical No 4
## 361 Research & Development Married Medical No 4
## 362 Research & Development Married Life Sciences No 4
## 363 Sales Single Medical No 2
## 364 Sales Single Marketing Yes 3
## 365 Research & Development Married Medical No 3
## 366 Research & Development Married Medical No 4
## 367 Sales Single Marketing Yes 3
## 368 Research & Development Single Technical Degree No 3
## 369 Sales Married Marketing Yes 2
## 370 Research & Development Single Life Sciences No 4
## 371 Sales Single Life Sciences Yes 3
## 372 Research & Development Single Life Sciences No 3
## 373 Research & Development Single Life Sciences No 4
## 374 Research & Development Divorced Medical No 2
## 375 Sales Single Life Sciences No 4
## 376 Research & Development Single Other No 3
## 377 Sales Married Life Sciences No 2
## 378 Research & Development Married Life Sciences No 3
## 379 Sales Single Marketing Yes 3
## 380 Research & Development Single Life Sciences No 3
## 381 Sales Divorced Marketing No 4
## 382 Sales Married Technical Degree No 1
## 383 Research & Development Single Technical Degree Yes 1
## 384 Research & Development Married Medical No 3
## 385 Sales Married Medical No 2
## 386 Research & Development Single Technical Degree Yes 3
## 387 Research & Development Divorced Life Sciences No 3
## 388 Sales Divorced Marketing No 2
## 389 Research & Development Divorced Life Sciences No 4
## 390 Research & Development Single Life Sciences No 4
## 391 Research & Development Divorced Life Sciences No 3
## 392 Research & Development Married Medical No 3
## 393 Research & Development Married Medical No 2
## 394 Sales Married Marketing No 4
## 395 Research & Development Married Medical No 2
## 396 Research & Development Married Medical No 3
## 397 Research & Development Divorced Other No 4
## 398 Sales Single Life Sciences No 2
## 399 Research & Development Married Medical No 5
## 400 Research & Development Married Life Sciences No 2
## 401 Research & Development Divorced Life Sciences No 1
## 402 Sales Married Life Sciences No 3
## 403 Sales Single Technical Degree No 3
## 404 Sales Married Marketing No 3
## 405 Research & Development Divorced Medical No 2
## 406 Research & Development Married Medical Yes 3
## 407 Research & Development Married Medical No 3
## 408 Research & Development Married Life Sciences No 2
## 409 Research & Development Married Life Sciences No 2
## 410 Research & Development Divorced Life Sciences No 2
## 411 Research & Development Single Life Sciences No 3
## 412 Research & Development Married Life Sciences No 3
## 413 Research & Development Divorced Medical No 3
## 414 Research & Development Married Technical Degree No 4
## 415 Sales Single Technical Degree Yes 1
## 416 Sales Divorced Marketing Yes 2
## 417 Research & Development Married Life Sciences No 2
## 418 Sales Married Life Sciences No 4
## 419 Research & Development Divorced Life Sciences No 3
## 420 Research & Development Married Life Sciences No 3
## 421 Research & Development Married Medical No 4
## 422 Research & Development Married Technical Degree Yes 5
## 423 Human Resources Single Technical Degree Yes 2
## 424 Sales Married Other No 4
## 425 Sales Divorced Marketing No 3
## 426 Research & Development Married Life Sciences No 4
## 427 Research & Development Single Medical No 3
## 428 Sales Married Marketing No 3
## 429 Research & Development Divorced Medical No 2
## 430 Research & Development Married Life Sciences No 3
## 431 Research & Development Single Life Sciences No 3
## 432 Research & Development Single Life Sciences No 4
## 433 Research & Development Divorced Life Sciences No 4
## 434 Sales Married Marketing No 3
## 435 Research & Development Divorced Life Sciences No 1
## 436 Research & Development Married Medical Yes 1
## 437 Research & Development Divorced Medical Yes 1
## 438 Sales Single Marketing No 1
## 439 Research & Development Married Life Sciences No 3
## 440 Research & Development Married Life Sciences Yes 3
## 441 Human Resources Divorced Human Resources Yes 3
## 442 Research & Development Married Other No 2
## 443 Sales Single Medical No 4
## 444 Research & Development Single Technical Degree Yes 1
## 445 Sales Married Marketing No 5
## 446 Sales Single Life Sciences No 5
## 447 Sales Single Life Sciences No 2
## 448 Sales Married Marketing No 3
## 449 Research & Development Single Life Sciences No 3
## 450 Research & Development Married Life Sciences No 1
## 451 Sales Single Life Sciences No 1
## 452 Research & Development Married Medical No 3
## 453 Sales Married Other No 3
## 454 Human Resources Divorced Life Sciences Yes 4
## 455 Research & Development Divorced Technical Degree No 3
## 456 Research & Development Divorced Medical No 5
## 457 Sales Divorced Life Sciences No 3
## 458 Sales Single Marketing Yes 3
## 459 Sales Divorced Other No 3
## 460 Research & Development Single Other No 4
## 461 Sales Divorced Medical No 2
## 462 Sales Single Medical No 3
## 463 Sales Single Life Sciences No 4
## 464 Research & Development Single Technical Degree Yes 3
## 465 Research & Development Single Technical Degree No 3
## 466 Research & Development Married Medical No 1
## 467 Sales Married Life Sciences No 5
## 468 Sales Divorced Medical No 4
## 469 Research & Development Divorced Technical Degree No 2
## 470 Sales Married Other Yes 4
## 471 Sales Married Medical No 3
## 472 Research & Development Married Medical No 3
## 473 Research & Development Married Life Sciences No 4
## 474 Research & Development Divorced Life Sciences No 4
## 475 Research & Development Married Medical No 3
## 476 Sales Married Marketing No 2
## 477 Research & Development Married Other No 2
## 478 Human Resources Married Medical No 3
## 479 Sales Married Medical No 1
## 480 Research & Development Married Life Sciences Yes 3
## 481 Sales Married Life Sciences Yes 4
## 482 Research & Development Married Life Sciences No 2
## 483 Sales Divorced Medical Yes 4
## 484 Research & Development Single Other No 2
## 485 Sales Divorced Medical No 4
## 486 Research & Development Divorced Medical No 4
## 487 Sales Married Marketing No 3
## 488 Research & Development Single Life Sciences No 3
## 489 Research & Development Married Life Sciences No 4
## 490 Research & Development Divorced Other No 4
## 491 Research & Development Single Life Sciences No 1
## 492 Research & Development Divorced Medical No 5
## 493 Research & Development Married Life Sciences No 4
## 494 Human Resources Single Life Sciences No 4
## 495 Sales Divorced Technical Degree No 3
## 496 Sales Divorced Marketing Yes 1
## 497 Sales Single Technical Degree No 1
## 498 Research & Development Married Other No 4
## 499 Research & Development Married Medical No 1
## 500 Sales Divorced Marketing No 4
## 501 Research & Development Married Life Sciences No 4
## 502 Research & Development Divorced Medical No 3
## 503 Sales Single Medical No 1
## 504 Research & Development Married Life Sciences No 5
## 505 Sales Married Life Sciences Yes 4
## 506 Research & Development Married Life Sciences No 3
## 507 Research & Development Married Other No 3
## 508 Sales Married Medical No 2
## 509 Research & Development Single Life Sciences No 4
## 510 Research & Development Divorced Life Sciences No 3
## 511 Human Resources Married Medical No 4
## 512 Research & Development Divorced Medical No 2
## 513 Research & Development Single Medical No 4
## 514 Research & Development Single Medical Yes 1
## 515 Research & Development Single Life Sciences Yes 3
## 516 Research & Development Married Life Sciences No 3
## 517 Research & Development Married Medical No 3
## 518 Sales Married Life Sciences No 3
## 519 Sales Single Marketing No 4
## 520 Research & Development Divorced Life Sciences No 4
## 521 Sales Married Marketing No 1
## 522 Sales Divorced Medical No 1
## 523 Research & Development Single Life Sciences No 2
## 524 Research & Development Married Medical No 1
## 525 Research & Development Single Medical No 3
## 526 Sales Single Life Sciences Yes 2
## 527 Research & Development Single Technical Degree No 4
## 528 Sales Single Marketing No 3
## 529 Sales Married Technical Degree Yes 2
## 530 Research & Development Single Life Sciences No 4
## 531 Research & Development Married Life Sciences No 2
## 532 Research & Development Single Life Sciences No 2
## 533 Sales Single Marketing No 4
## 534 Sales Married Life Sciences No 4
## 535 Research & Development Married Life Sciences No 3
## 536 Human Resources Divorced Human Resources No 4
## 537 Sales Single Marketing No 4
## 538 Research & Development Divorced Life Sciences No 2
## 539 Human Resources Married Human Resources No 3
## 540 Sales Married Marketing No 4
## 541 Research & Development Single Life Sciences Yes 2
## 542 Research & Development Married Life Sciences No 3
## 543 Research & Development Single Life Sciences No 3
## 544 Research & Development Single Medical No 3
## 545 Sales Divorced Medical No 3
## 546 Sales Divorced Marketing No 5
## 547 Sales Single Life Sciences No 3
## 548 Research & Development Divorced Medical Yes 3
## 549 Sales Married Life Sciences No 3
## 550 Research & Development Single Medical No 2
## 551 Research & Development Married Medical No 1
## 552 Human Resources Married Human Resources No 3
## 553 Research & Development Married Medical No 3
## 554 Research & Development Single Medical No 1
## 555 Research & Development Single Medical No 3
## 556 Sales Divorced Marketing No 3
## 557 Research & Development Single Life Sciences No 3
## 558 Research & Development Divorced Life Sciences No 4
## 559 Research & Development Married Life Sciences No 4
## 560 Research & Development Married Medical No 5
## 561 Research & Development Divorced Life Sciences No 5
## 562 Sales Married Marketing No 4
## 563 Research & Development Single Other Yes 4
## 564 Sales Single Medical No 1
## 565 Sales Single Technical Degree No 2
## 566 Research & Development Single Medical No 1
## 567 Sales Single Life Sciences Yes 2
## 568 Sales Single Other No 3
## 569 Research & Development Married Medical Yes 3
## 570 Sales Single Life Sciences No 4
## 571 Research & Development Married Medical No 4
## 572 Research & Development Divorced Life Sciences No 2
## 573 Research & Development Married Medical No 3
## 574 Sales Single Technical Degree Yes 3
## 575 Research & Development Single Life Sciences No 4
## 576 Research & Development Divorced Medical No 4
## 577 Sales Married Marketing No 1
## 578 Research & Development Divorced Life Sciences No 1
## 579 Research & Development Single Life Sciences No 4
## 580 Research & Development Single Medical No 4
## 581 Sales Married Life Sciences No 4
## 582 Research & Development Married Life Sciences No 3
## 583 Research & Development Married Medical No 2
## 584 Sales Married Life Sciences No 2
## 585 Research & Development Divorced Life Sciences No 3
## 586 Research & Development Married Life Sciences Yes 3
## 587 Research & Development Divorced Life Sciences No 3
## 588 Research & Development Married Life Sciences No 4
## 589 Research & Development Married Medical No 3
## 590 Research & Development Married Life Sciences Yes 2
## 591 Research & Development Married Medical No 3
## 592 Sales Single Marketing Yes 3
## 593 Research & Development Married Other No 2
## 594 Research & Development Married Other No 3
## 595 Research & Development Married Life Sciences No 2
## 596 Research & Development Single Life Sciences Yes 4
## 597 Research & Development Single Life Sciences No 4
## 598 Research & Development Married Life Sciences No 2
## 599 Research & Development Single Medical Yes 4
## 600 Human Resources Married Human Resources No 3
## 601 Research & Development Married Life Sciences No 3
## 602 Research & Development Single Medical No 4
## 603 Research & Development Single Medical No 3
## 604 Research & Development Single Life Sciences No 3
## 605 Research & Development Married Life Sciences No 3
## 606 Research & Development Divorced Life Sciences No 3
## 607 Research & Development Single Life Sciences No 4
## 608 Sales Married Marketing Yes 3
## 609 Sales Single Medical Yes 1
## 610 Research & Development Married Life Sciences No 2
## 611 Research & Development Divorced Technical Degree No 1
## 612 Research & Development Single Other No 3
## 613 Sales Married Marketing No 4
## 614 Human Resources Married Human Resources No 2
## 615 Research & Development Married Medical Yes 2
## 616 Research & Development Married Medical No 3
## 617 Sales Married Marketing No 4
## 618 Research & Development Single Medical No 3
## 619 Research & Development Single Medical No 1
## 620 Sales Divorced Medical No 3
## 621 Research & Development Single Medical No 1
## 622 Sales Married Life Sciences No 2
## 623 Sales Divorced Life Sciences No 4
## 624 Research & Development Divorced Life Sciences No 4
## 625 Sales Married Marketing No 2
## 626 Sales Divorced Marketing No 3
## 627 Research & Development Married Medical No 2
## 628 Research & Development Married Medical No 4
## 629 Sales Divorced Marketing No 4
## 630 Human Resources Divorced Medical No 2
## 631 Research & Development Married Life Sciences No 2
## 632 Research & Development Married Life Sciences No 4
## 633 Research & Development Single Medical No 1
## 634 Human Resources Married Life Sciences No 3
## 635 Sales Married Other No 1
## 636 Research & Development Married Life Sciences No 3
## 637 Research & Development Divorced Life Sciences Yes 4
## 638 Research & Development Divorced Life Sciences No 3
## 639 Sales Married Marketing No 1
## 640 Research & Development Married Technical Degree No 3
## 641 Research & Development Married Life Sciences No 1
## 642 Sales Married Life Sciences No 2
## 643 Sales Married Marketing No 3
## 644 Research & Development Married Life Sciences No 3
## 645 Research & Development Married Life Sciences No 4
## 646 Sales Divorced Medical Yes 3
## 647 Sales Married Marketing No 3
## 648 Research & Development Married Technical Degree No 3
## 649 Sales Married Medical No 2
## 650 Research & Development Single Life Sciences No 4
## 651 Research & Development Married Life Sciences No 3
## 652 Sales Married Marketing No 2
## 653 Sales Single Medical No 2
## 654 Research & Development Divorced Life Sciences No 4
## 655 Human Resources Married Life Sciences No 3
## 656 Human Resources Divorced Human Resources No 2
## 657 Research & Development Single Life Sciences Yes 4
## 658 Research & Development Divorced Medical No 1
## 659 Research & Development Married Life Sciences No 2
## 660 Sales Single Medical No 4
## 661 Research & Development Divorced Life Sciences Yes 1
## 662 Research & Development Divorced Life Sciences No 3
## 663 Sales Single Medical Yes 3
## 664 Research & Development Single Other Yes 1
## 665 Research & Development Married Life Sciences No 1
## 666 Sales Single Life Sciences No 4
## 667 Research & Development Married Life Sciences Yes 1
## 668 Research & Development Divorced Life Sciences Yes 4
## 669 Research & Development Divorced Medical No 3
## 670 Research & Development Married Medical Yes 3
## 671 Research & Development Single Life Sciences No 3
## 672 Research & Development Divorced Life Sciences No 3
## 673 Sales Single Medical No 2
## 674 Research & Development Single Other No 4
## 675 Research & Development Divorced Technical Degree No 3
## 676 Sales Married Life Sciences No 4
## 677 Research & Development Married Life Sciences No 1
## 678 Research & Development Married Other No 2
## 679 Research & Development Married Medical No 4
## 680 Sales Married Marketing No 2
## 681 Research & Development Single Other No 4
## 682 Research & Development Married Technical Degree No 3
## 683 Research & Development Married Life Sciences No 3
## 684 Sales Married Marketing Yes 2
## 685 Sales Divorced Marketing No 4
## 686 Sales Single Medical No 3
## 687 Research & Development Single Medical No 3
## 688 Research & Development Single Medical No 4
## 689 Sales Single Other Yes 3
## 690 Research & Development Single Technical Degree Yes 3
## 691 Research & Development Married Medical No 3
## 692 Research & Development Divorced Medical No 4
## 693 Research & Development Married Medical No 4
## 694 Sales Married Life Sciences Yes 1
## 695 Research & Development Single Life Sciences No 3
## 696 Sales Married Life Sciences Yes 4
## 697 Research & Development Married Life Sciences No 2
## 698 Sales Married Technical Degree No 3
## 699 Sales Married Medical No 3
## 700 Research & Development Married Life Sciences No 2
## 701 Research & Development Single Technical Degree Yes 3
## 702 Sales Divorced Medical No 2
## 703 Sales Divorced Other No 2
## 704 Sales Single Technical Degree No 3
## 705 Sales Divorced Life Sciences No 4
## 706 Sales Single Life Sciences No 5
## 707 Sales Single Life Sciences Yes 3
## 708 Research & Development Divorced Medical No 4
## 709 Sales Divorced Technical Degree No 4
## 710 Research & Development Single Medical Yes 2
## 711 Sales Single Life Sciences No 3
## 712 Research & Development Single Life Sciences Yes 3
## 713 Research & Development Single Life Sciences No 1
## 714 Research & Development Divorced Medical No 4
## 715 Research & Development Divorced Medical No 2
## 716 Research & Development Married Other No 4
## 717 Research & Development Divorced Medical No 3
## 718 Research & Development Married Technical Degree No 4
## 719 Research & Development Married Life Sciences No 2
## 720 Sales Single Life Sciences No 2
## 721 Research & Development Married Life Sciences Yes 3
## 722 Research & Development Married Life Sciences No 3
## 723 Research & Development Married Medical No 1
## 724 Research & Development Divorced Medical No 2
## 725 Research & Development Divorced Medical No 1
## 726 Research & Development Divorced Other Yes 4
## 727 Research & Development Married Life Sciences No 1
## 728 Research & Development Single Life Sciences No 2
## 729 Research & Development Married Technical Degree No 3
## 730 Research & Development Divorced Medical No 4
## 731 Research & Development Married Life Sciences No 2
## 732 Research & Development Single Medical Yes 3
## 733 Research & Development Single Medical Yes 3
## 734 Research & Development Married Medical No 2
## 735 Research & Development Married Life Sciences No 1
## 736 Research & Development Single Life Sciences No 3
## 737 Research & Development Single Life Sciences No 4
## 738 Research & Development Single Medical No 2
## 739 Research & Development Married Life Sciences No 1
## 740 Research & Development Married Life Sciences No 4
## 741 Research & Development Divorced Other No 3
## 742 Sales Married Marketing No 2
## 743 Research & Development Married Life Sciences No 3
## 744 Research & Development Single Life Sciences No 3
## 745 Research & Development Married Medical Yes 2
## 746 Research & Development Married Medical No 4
## 747 Research & Development Divorced Life Sciences No 1
## 748 Sales Single Life Sciences No 4
## 749 Sales Single Medical Yes 2
## 750 Sales Married Marketing Yes 1
## 751 Sales Married Medical No 3
## 752 Sales Married Life Sciences No 3
## 753 Research & Development Single Life Sciences Yes 4
## 754 Research & Development Single Medical No 3
## 755 Sales Single Life Sciences No 1
## 756 Sales Married Life Sciences No 2
## 757 Research & Development Single Medical No 4
## 758 Sales Divorced Marketing No 4
## 759 Sales Married Technical Degree No 2
## 760 Human Resources Single Medical No 4
## 761 Sales Married Marketing No 3
## 762 Research & Development Divorced Other Yes 3
## 763 Research & Development Married Life Sciences Yes 3
## 764 Sales Married Life Sciences No 4
## 765 Sales Married Medical No 1
## 766 Research & Development Married Other No 4
## 767 Research & Development Married Medical No 4
## 768 Research & Development Single Other No 3
## 769 Sales Married Marketing No 3
## 770 Research & Development Divorced Medical No 1
## 771 Research & Development Divorced Medical No 4
## 772 Sales Married Life Sciences No 4
## 773 Research & Development Married Medical No 3
## 774 Research & Development Single Medical No 5
## 775 Research & Development Single Medical No 1
## 776 Sales Divorced Medical No 3
## 777 Sales Single Marketing Yes 3
## 778 Research & Development Single Life Sciences Yes 3
## 779 Research & Development Divorced Life Sciences No 4
## 780 Research & Development Married Life Sciences Yes 4
## 781 Research & Development Single Technical Degree Yes 2
## 782 Research & Development Married Medical No 2
## 783 Research & Development Married Other No 3
## 784 Research & Development Married Technical Degree No 2
## 785 Research & Development Married Life Sciences No 1
## 786 Research & Development Married Technical Degree No 4
## 787 Research & Development Married Life Sciences No 5
## 788 Research & Development Married Life Sciences No 1
## 789 Research & Development Single Other No 3
## 790 Human Resources Married Medical Yes 2
## 791 Research & Development Divorced Life Sciences No 3
## 792 Sales Single Technical Degree Yes 3
## 793 Research & Development Single Medical Yes 4
## 794 Research & Development Divorced Life Sciences No 2
## 795 Research & Development Single Life Sciences No 1
## 796 Sales Divorced Life Sciences No 4
## 797 Research & Development Married Technical Degree Yes 1
## 798 Research & Development Divorced Medical Yes 3
## 799 Research & Development Single Medical Yes 3
## 800 Research & Development Married Medical No 2
## 801 Research & Development Divorced Medical Yes 3
## 802 Sales Single Other Yes 4
## 803 Sales Married Life Sciences No 3
## 804 Research & Development Married Life Sciences No 4
## 805 Research & Development Single Medical No 4
## 806 Sales Married Life Sciences No 4
## 807 Research & Development Single Life Sciences No 4
## 808 Sales Divorced Marketing No 4
## 809 Research & Development Divorced Life Sciences No 4
## 810 Research & Development Divorced Medical No 3
## 811 Sales Married Marketing No 1
## 812 Sales Single Marketing No 2
## 813 Research & Development Married Life Sciences No 3
## 814 Research & Development Divorced Life Sciences Yes 3
## 815 Research & Development Single Medical No 3
## 816 Research & Development Single Technical Degree No 1
## 817 Research & Development Single Life Sciences No 3
## 818 Research & Development Single Life Sciences No 4
## 819 Sales Married Life Sciences No 3
## 820 Research & Development Married Life Sciences No 1
## 821 Sales Divorced Marketing No 2
## 822 Sales Married Technical Degree No 4
## 823 Research & Development Single Life Sciences No 2
## 824 Research & Development Divorced Life Sciences No 3
## 825 Research & Development Single Medical No 3
## 826 Research & Development Married Medical No 1
## 827 Human Resources Married Human Resources No 3
## 828 Research & Development Divorced Life Sciences No 3
## 829 Research & Development Single Medical Yes 1
## 830 Sales Single Marketing Yes 4
## 831 Research & Development Married Life Sciences No 4
## 832 Research & Development Married Medical Yes 3
## 833 Research & Development Divorced Medical No 2
## 834 Research & Development Married Life Sciences No 3
## 835 Sales Married Life Sciences No 1
## 836 Human Resources Single Technical Degree No 4
## 837 Sales Married Life Sciences Yes 1
## 838 Research & Development Single Medical No 4
## 839 Sales Single Life Sciences Yes 3
## 840 Sales Single Marketing No 4
## 841 Research & Development Married Medical No 4
## 842 Research & Development Single Medical No 3
## 843 Research & Development Married Life Sciences Yes 1
## 844 Research & Development Married Medical No 4
## 845 Sales Married Marketing No 3
## 846 Research & Development Married Medical No 2
## 847 Research & Development Divorced Life Sciences No 3
## 848 Research & Development Single Medical No 3
## 849 Research & Development Married Other No 4
## 850 Sales Single Marketing Yes 3
## 851 Sales Divorced Life Sciences No 1
## 852 Research & Development Divorced Technical Degree No 4
## 853 Research & Development Married Medical No 1
## 854 Research & Development Single Life Sciences No 2
## 855 Research & Development Married Medical No 3
## 856 Research & Development Married Life Sciences No 3
## 857 Research & Development Single Life Sciences No 3
## 858 Research & Development Single Life Sciences Yes 4
## 859 Research & Development Divorced Medical No 2
## 860 Research & Development Married Life Sciences No 1
## 861 Research & Development Married Life Sciences Yes 4
## 862 Sales Married Marketing No 3
## 863 Research & Development Single Life Sciences No 3
## 864 Human Resources Married Human Resources No 3
## 865 Research & Development Divorced Life Sciences Yes 2
## 866 Sales Divorced Life Sciences No 4
## 867 Sales Married Medical No 4
## 868 Research & Development Married Medical No 3
## 869 Research & Development Married Medical No 4
## 870 Research & Development Married Life Sciences No 2
## 871 Sales Married Life Sciences No 4
## 872 Research & Development Married Life Sciences Yes 2
## 873 Sales Married Medical No 3
## 874 Research & Development Divorced Life Sciences No 4
## 875 Research & Development Divorced Life Sciences No 4
## 876 Research & Development Single Other No 4
## 877 Sales Single Marketing No 3
## 878 Research & Development Divorced Technical Degree No 4
## 879 Human Resources Married Medical No 5
## 880 Sales Divorced Marketing No 4
## 881 Research & Development Married Other No 3
## 882 Research & Development Single Life Sciences No 2
## 883 Research & Development Divorced Technical Degree No 3
## 884 Research & Development Married Medical No 3
## 885 Sales Divorced Technical Degree No 3
## 886 Sales Single Life Sciences No 4
## 887 Research & Development Married Medical No 3
## 888 Research & Development Married Medical No 5
## 889 Sales Married Marketing No 2
## 890 Research & Development Married Life Sciences No 3
## 891 Research & Development Divorced Life Sciences No 4
## 892 Research & Development Married Life Sciences No 1
## 893 Research & Development Single Medical Yes 3
## 894 Research & Development Divorced Life Sciences No 3
## 895 Research & Development Married Life Sciences No 3
## 896 Research & Development Married Medical No 2
## 897 Research & Development Single Medical No 3
## 898 Sales Single Life Sciences No 3
## 899 Research & Development Married Life Sciences No 3
## 900 Research & Development Married Medical No 2
## 901 Research & Development Married Technical Degree No 3
## 902 Research & Development Single Technical Degree No 2
## 903 Research & Development Divorced Life Sciences No 2
## 904 Research & Development Divorced Life Sciences No 3
## 905 Research & Development Single Life Sciences No 3
## 906 Research & Development Divorced Life Sciences No 3
## 907 Research & Development Married Technical Degree No 3
## 908 Sales Married Marketing No 3
## 909 Sales Divorced Marketing No 5
## 910 Research & Development Single Life Sciences No 3
## 911 Research & Development Married Life Sciences No 2
## 912 Sales Single Life Sciences Yes 1
## 913 Research & Development Single Life Sciences No 2
## 914 Sales Single Marketing Yes 3
## 915 Research & Development Divorced Medical No 1
## 916 Research & Development Single Life Sciences Yes 2
## 917 Sales Married Marketing No 2
## 918 Sales Single Marketing No 3
## 919 Sales Divorced Life Sciences No 3
## 920 Research & Development Single Medical No 4
## 921 Research & Development Divorced Medical No 3
## 922 Research & Development Single Medical No 4
## 923 Research & Development Divorced Life Sciences No 2
## 924 Human Resources Married Life Sciences No 3
## 925 Research & Development Married Life Sciences No 1
## 926 Research & Development Married Medical No 4
## 927 Sales Single Marketing No 4
## 928 Research & Development Single Life Sciences No 4
## 929 Research & Development Married Medical Yes 3
## 930 Research & Development Married Life Sciences No 3
## 931 Research & Development Single Medical No 2
## 932 Research & Development Single Medical No 2
## 933 Research & Development Divorced Technical Degree Yes 3
## 934 Research & Development Single Technical Degree No 3
## 935 Research & Development Single Medical No 3
## 936 Sales Married Medical No 3
## 937 Research & Development Single Medical No 3
## 938 Research & Development Divorced Medical No 4
## 939 Research & Development Divorced Life Sciences No 4
## 940 Research & Development Married Life Sciences Yes 2
## 941 Research & Development Single Medical Yes 3
## 942 Research & Development Married Technical Degree No 3
## 943 Research & Development Married Technical Degree No 4
## 944 Human Resources Single Life Sciences No 2
## 945 Research & Development Married Life Sciences No 3
## 946 Research & Development Married Life Sciences No 3
## 947 Sales Single Marketing Yes 4
## 948 Sales Single Life Sciences Yes 3
## 949 Research & Development Married Medical No 4
## 950 Research & Development Single Life Sciences No 2
## 951 Sales Divorced Life Sciences No 4
## 952 Sales Single Medical No 2
## 953 Sales Single Life Sciences Yes 3
## 954 Research & Development Married Life Sciences Yes 3
## 955 Research & Development Married Life Sciences No 1
## 956 Research & Development Married Medical No 2
## 957 Human Resources Single Life Sciences No 4
## 958 Research & Development Divorced Life Sciences No 2
## 959 Research & Development Divorced Life Sciences No 3
## 960 Research & Development Single Life Sciences No 3
## 961 Sales Divorced Marketing No 3
## 962 Research & Development Single Life Sciences No 4
## 963 Human Resources Divorced Life Sciences No 3
## 964 Sales Divorced Life Sciences No 2
## 965 Sales Single Medical No 2
## 966 Research & Development Married Medical No 1
## 967 Research & Development Married Medical Yes 4
## 968 Research & Development Married Life Sciences No 4
## 969 Sales Married Marketing No 3
## 970 Research & Development Single Life Sciences No 3
## 971 Sales Married Medical No 3
## 972 Research & Development Single Technical Degree No 2
## 973 Research & Development Single Life Sciences No 3
## 974 Research & Development Married Medical No 3
## 975 Sales Single Life Sciences No 1
## 976 Sales Single Marketing Yes 4
## 977 Research & Development Married Life Sciences No 3
## 978 Research & Development Divorced Technical Degree No 1
## 979 Research & Development Divorced Medical No 1
## 980 Research & Development Married Medical No 3
## 981 Sales Single Life Sciences Yes 3
## 982 Sales Married Marketing Yes 4
## 983 Research & Development Divorced Life Sciences No 3
## 984 Research & Development Single Technical Degree No 4
## 985 Sales Married Life Sciences No 3
## 986 Research & Development Married Medical Yes 4
## 987 Sales Married Life Sciences No 4
## 988 Sales Married Marketing No 3
## 989 Research & Development Divorced Life Sciences No 3
## 990 Research & Development Married Life Sciences No 1
## 991 Sales Married Life Sciences No 1
## 992 Sales Married Marketing No 1
## 993 Research & Development Married Life Sciences No 2
## 994 Sales Married Life Sciences No 1
## 995 Research & Development Married Medical No 2
## 996 Research & Development Single Medical No 3
## 997 Sales Married Marketing No 3
## 998 Research & Development Single Life Sciences Yes 4
## 999 Research & Development Single Medical No 1
## 1000 Human Resources Married Human Resources No 3
## 1001 Research & Development Married Other No 4
## 1002 Research & Development Single Medical No 3
## 1003 Research & Development Single Life Sciences No 2
## 1004 Research & Development Married Technical Degree No 3
## 1005 Research & Development Single Other No 3
## 1006 Human Resources Single Other No 3
## 1007 Research & Development Single Life Sciences Yes 2
## 1008 Research & Development Single Other Yes 1
## 1009 Research & Development Single Medical No 3
## 1010 Research & Development Married Medical No 3
## 1011 Research & Development Divorced Medical No 4
## 1012 Sales Single Marketing No 4
## 1013 Sales Single Life Sciences Yes 4
## 1014 Sales Divorced Marketing No 4
## 1015 Research & Development Single Life Sciences No 5
## 1016 Research & Development Divorced Other No 4
## 1017 Research & Development Single Life Sciences Yes 3
## 1018 Research & Development Married Life Sciences No 1
## 1019 Research & Development Single Life Sciences No 4
## 1020 Sales Married Marketing No 4
## 1021 Research & Development Married Technical Degree No 3
## 1022 Sales Married Life Sciences Yes 2
## 1023 Research & Development Single Technical Degree No 2
## 1024 Research & Development Married Life Sciences No 2
## 1025 Research & Development Married Medical No 4
## 1026 Sales Married Medical No 1
## 1027 Sales Married Marketing No 5
## 1028 Research & Development Married Life Sciences No 3
## 1029 Research & Development Married Medical No 5
## 1030 Research & Development Divorced Other No 4
## 1031 Sales Divorced Life Sciences No 2
## 1032 Sales Divorced Marketing Yes 3
## 1033 Research & Development Single Life Sciences Yes 3
## 1034 Research & Development Single Life Sciences Yes 5
## 1035 Research & Development Divorced Medical No 3
## 1036 Human Resources Single Medical No 2
## 1037 Research & Development Married Life Sciences Yes 3
## 1038 Research & Development Married Technical Degree No 3
## 1039 Sales Divorced Marketing No 3
## 1040 Human Resources Married Technical Degree Yes 4
## 1041 Research & Development Divorced Medical No 1
## 1042 Sales Single Medical No 3
## 1043 Research & Development Single Life Sciences No 3
## 1044 Research & Development Single Medical No 3
## 1045 Research & Development Married Technical Degree No 4
## 1046 Research & Development Divorced Medical No 3
## 1047 Research & Development Single Life Sciences No 3
## 1048 Sales Married Medical No 3
## 1049 Sales Single Other No 3
## 1050 Sales Married Life Sciences No 1
## 1051 Research & Development Single Medical No 2
## 1052 Sales Married Marketing No 5
## 1053 Research & Development Divorced Technical Degree No 3
## 1054 Research & Development Married Life Sciences No 2
## 1055 Research & Development Divorced Life Sciences No 4
## 1056 Research & Development Divorced Medical No 3
## 1057 Sales Married Technical Degree Yes 3
## 1058 Sales Single Technical Degree Yes 3
## 1059 Sales Single Medical Yes 4
## 1060 Sales Married Life Sciences No 1
## 1061 Research & Development Single Medical Yes 3
## 1062 Sales Married Life Sciences No 2
## 1063 Research & Development Single Medical No 1
## 1064 Sales Divorced Life Sciences No 3
## 1065 Human Resources Divorced Life Sciences No 3
## 1066 Research & Development Married Life Sciences No 4
## 1067 Research & Development Married Medical No 4
## 1068 Sales Married Medical No 3
## 1069 Research & Development Single Medical Yes 2
## 1070 Research & Development Divorced Life Sciences No 3
## 1071 Sales Single Life Sciences No 3
## 1072 Research & Development Married Medical No 2
## 1073 Research & Development Married Life Sciences No 1
## 1074 Research & Development Married Life Sciences No 1
## 1075 Research & Development Single Life Sciences No 5
## 1076 Research & Development Single Medical No 3
## 1077 Research & Development Divorced Medical No 4
## 1078 Research & Development Single Technical Degree Yes 4
## 1079 Research & Development Married Life Sciences No 3
## 1080 Research & Development Single Life Sciences No 3
## 1081 Sales Married Life Sciences No 3
## 1082 Research & Development Single Life Sciences No 3
## 1083 Research & Development Single Life Sciences No 1
## 1084 Research & Development Single Life Sciences Yes 4
## 1085 Sales Married Technical Degree No 3
## 1086 Research & Development Single Life Sciences Yes 3
## 1087 Research & Development Single Medical No 5
## 1088 Sales Married Technical Degree No 2
## 1089 Research & Development Married Medical No 3
## 1090 Research & Development Married Medical No 3
## 1091 Research & Development Married Other No 1
## 1092 Research & Development Single Life Sciences No 3
## 1093 Research & Development Married Technical Degree No 3
## 1094 Research & Development Married Life Sciences No 3
## 1095 Sales Married Medical No 2
## 1096 Research & Development Married Life Sciences No 4
## 1097 Human Resources Single Medical No 2
## 1098 Research & Development Divorced Technical Degree No 2
## 1099 Research & Development Divorced Life Sciences No 2
## 1100 Research & Development Divorced Technical Degree No 4
## 1101 Sales Married Life Sciences No 4
## 1102 Research & Development Married Life Sciences No 2
## 1103 Sales Single Life Sciences No 4
## 1104 Sales Divorced Life Sciences No 4
## 1105 Research & Development Married Life Sciences No 3
## 1106 Sales Married Life Sciences No 4
## 1107 Sales Married Life Sciences Yes 3
## 1108 Human Resources Married Human Resources No 4
## 1109 Research & Development Single Medical No 3
## 1110 Sales Married Technical Degree No 4
## 1111 Research & Development Divorced Life Sciences Yes 3
## 1112 Research & Development Married Technical Degree Yes 5
## 1113 Research & Development Married Medical Yes 3
## 1114 Research & Development Married Technical Degree No 4
## 1115 Research & Development Married Other No 4
## 1116 Research & Development Single Medical No 4
## 1117 Sales Married Marketing No 5
## 1118 Research & Development Married Life Sciences No 4
## 1119 Research & Development Married Life Sciences No 3
## 1120 Sales Married Life Sciences No 3
## 1121 Sales Single Life Sciences No 3
## 1122 Sales Single Life Sciences No 4
## 1123 Research & Development Single Medical No 1
## 1124 Research & Development Single Medical No 4
## 1125 Sales Married Medical No 3
## 1126 Research & Development Divorced Life Sciences No 1
## 1127 Sales Married Marketing No 3
## 1128 Research & Development Married Technical Degree No 3
## 1129 Research & Development Married Life Sciences No 4
## 1130 Research & Development Single Other No 2
## 1131 Research & Development Married Life Sciences No 3
## 1132 Research & Development Married Technical Degree No 4
## 1133 Sales Married Life Sciences No 2
## 1134 Research & Development Divorced Technical Degree No 3
## 1135 Research & Development Married Life Sciences No 2
## 1136 Sales Single Life Sciences No 4
## 1137 Research & Development Married Medical Yes 3
## 1138 Research & Development Married Other No 2
## 1139 Research & Development Married Medical No 5
## 1140 Research & Development Married Other No 4
## 1141 Research & Development Divorced Medical No 3
## 1142 Research & Development Married Medical No 3
## 1143 Research & Development Single Medical No 5
## 1144 Sales Married Marketing No 3
## 1145 Sales Single Other No 4
## 1146 Research & Development Married Life Sciences No 4
## 1147 Research & Development Divorced Life Sciences No 4
## 1148 Research & Development Married Life Sciences No 4
## 1149 Research & Development Married Medical No 5
## 1150 Research & Development Divorced Other No 3
## 1151 Research & Development Married Life Sciences No 5
## 1152 Research & Development Divorced Medical No 3
## 1153 Research & Development Single Medical No 1
## 1154 Sales Single Medical Yes 2
## 1155 Human Resources Married Life Sciences No 4
## 1156 Research & Development Divorced Medical No 2
## 1157 Research & Development Married Life Sciences No 3
## 1158 Research & Development Married Life Sciences No 4
## 1159 Research & Development Married Life Sciences No 3
## 1160 Research & Development Single Medical No 3
## 1161 Research & Development Divorced Other No 2
## 1162 Research & Development Married Medical No 2
## 1163 Sales Married Medical Yes 3
## 1164 Research & Development Married Medical No 3
## 1165 Research & Development Single Life Sciences No 3
## 1166 Human Resources Married Human Resources No 5
## 1167 Research & Development Married Medical No 5
## 1168 Sales Divorced Medical Yes 2
## 1169 Research & Development Single Technical Degree No 1
## 1170 Research & Development Married Medical No 3
## 1171 Research & Development Single Medical No 3
## 1172 Research & Development Single Life Sciences Yes 3
## 1173 Sales Single Medical No 3
## 1174 Research & Development Married Life Sciences No 4
## 1175 Research & Development Divorced Life Sciences No 1
## 1176 Research & Development Married Medical No 3
## 1177 Research & Development Married Other No 4
## 1178 Research & Development Divorced Life Sciences No 5
## 1179 Sales Single Medical No 3
## 1180 Research & Development Divorced Life Sciences No 3
## 1181 Research & Development Single Life Sciences No 3
## 1182 Research & Development Married Life Sciences No 1
## 1183 Research & Development Married Medical No 4
## 1184 Research & Development Divorced Life Sciences No 2
## 1185 Research & Development Married Medical No 5
## 1186 Research & Development Married Life Sciences No 2
## 1187 Sales Single Other Yes 4
## 1188 Research & Development Married Life Sciences No 3
## 1189 Sales Divorced Medical No 3
## 1190 Sales Divorced Medical No 4
## 1191 Research & Development Divorced Medical No 3
## 1192 Sales Married Life Sciences No 4
## 1193 Research & Development Divorced Medical No 3
## 1194 Research & Development Single Medical No 3
## 1195 Sales Divorced Life Sciences No 4
## 1196 Research & Development Single Life Sciences No 3
## 1197 Sales Single Life Sciences No 2
## 1198 Sales Single Life Sciences No 1
## 1199 Sales Divorced Life Sciences No 3
## 1200 Research & Development Married Life Sciences No 4
## 1201 Human Resources Divorced Life Sciences No 3
## 1202 Research & Development Single Medical Yes 1
## 1203 Research & Development Married Medical No 2
## 1204 Research & Development Married Medical No 4
## 1205 Sales Married Medical Yes 2
## 1206 Research & Development Single Life Sciences Yes 4
## 1207 Research & Development Single Medical No 3
## 1208 Research & Development Divorced Technical Degree No 3
## 1209 Research & Development Married Medical No 2
## 1210 Research & Development Divorced Medical No 4
## 1211 Research & Development Married Medical No 3
## 1212 Sales Divorced Medical No 4
## 1213 Research & Development Married Life Sciences No 3
## 1214 Sales Divorced Life Sciences Yes 3
## 1215 Research & Development Married Life Sciences No 3
## 1216 Research & Development Single Medical No 4
## 1217 Sales Married Medical No 3
## 1218 Research & Development Married Medical No 3
## 1219 Sales Single Marketing No 3
## 1220 Research & Development Married Medical No 4
## 1221 Sales Single Life Sciences No 4
## 1222 Research & Development Married Life Sciences No 1
## 1223 Human Resources Married Human Resources Yes 1
## 1224 Sales Married Life Sciences Yes 3
## 1225 Research & Development Married Medical No 4
## 1226 Research & Development Single Technical Degree No 2
## 1227 Research & Development Married Life Sciences No 3
## 1228 Research & Development Married Life Sciences No 4
## 1229 Human Resources Married Human Resources No 3
## 1230 Research & Development Married Life Sciences No 2
## 1231 Research & Development Divorced Medical No 1
## 1232 Research & Development Single Life Sciences No 4
## 1233 Research & Development Married Life Sciences No 4
## 1234 Research & Development Married Life Sciences No 1
## 1235 Sales Married Marketing No 4
## 1236 Sales Divorced Life Sciences No 3
## 1237 Sales Divorced Marketing Yes 5
## 1238 Sales Single Life Sciences Yes 2
## 1239 Research & Development Single Medical No 1
## 1240 Research & Development Single Technical Degree No 1
## 1241 Research & Development Married Life Sciences No 3
## 1242 Sales Married Life Sciences No 3
## 1243 Sales Single Medical No 4
## 1244 Human Resources Married Life Sciences No 3
## 1245 Research & Development Single Technical Degree No 4
## 1246 Human Resources Married Medical No 3
## 1247 Human Resources Divorced Human Resources Yes 3
## 1248 Sales Married Technical Degree No 3
## 1249 Research & Development Single Medical No 3
## 1250 Sales Single Marketing Yes 3
## 1251 Research & Development Single Life Sciences No 3
## 1252 Sales Divorced Marketing No 2
## 1253 Research & Development Married Medical No 4
## 1254 Sales Single Marketing No 3
## 1255 Sales Single Marketing No 4
## 1256 Sales Single Life Sciences Yes 3
## 1257 Research & Development Married Medical No 2
## 1258 Sales Married Marketing Yes 4
## 1259 Research & Development Divorced Technical Degree No 3
## 1260 Research & Development Married Life Sciences No 3
## 1261 Research & Development Single Technical Degree No 4
## 1262 Research & Development Married Medical No 3
## 1263 Research & Development Married Technical Degree Yes 3
## 1264 Research & Development Divorced Medical No 3
## 1265 Research & Development Married Medical No 3
## 1266 Research & Development Divorced Technical Degree No 3
## 1267 Research & Development Divorced Life Sciences No 4
## 1268 Sales Divorced Life Sciences No 3
## 1269 Research & Development Married Medical No 4
## 1270 Human Resources Single Life Sciences No 3
## 1271 Sales Single Life Sciences No 2
## 1272 Sales Single Marketing Yes 1
## 1273 Research & Development Married Other No 2
## 1274 Research & Development Married Medical Yes 1
## 1275 Sales Married Marketing No 4
## 1276 Research & Development Married Technical Degree No 3
## 1277 Sales Married Marketing No 2
## 1278 Research & Development Divorced Medical No 4
## 1279 Research & Development Married Life Sciences No 3
## 1280 Research & Development Divorced Medical Yes 2
## 1281 Human Resources Divorced Other No 2
## 1282 Sales Single Life Sciences Yes 3
## 1283 Research & Development Married Life Sciences No 4
## 1284 Research & Development Married Life Sciences No 3
## 1285 Research & Development Single Medical No 1
## 1286 Sales Single Life Sciences No 2
## 1287 Research & Development Married Life Sciences No 2
## 1288 Research & Development Married Medical No 3
## 1289 Research & Development Divorced Medical No 2
## 1290 Human Resources Divorced Human Resources No 3
## 1291 Research & Development Married Life Sciences Yes 4
## 1292 Research & Development Single Medical Yes 4
## 1293 Sales Divorced Life Sciences No 3
## 1294 Research & Development Single Life Sciences No 3
## 1295 Research & Development Single Life Sciences No 3
## 1296 Sales Divorced Marketing No 1
## 1297 Research & Development Single Medical No 3
## 1298 Human Resources Married Medical Yes 2
## 1299 Research & Development Married Medical Yes 2
## 1300 Research & Development Divorced Life Sciences No 3
## 1301 Sales Married Technical Degree No 2
## 1302 Sales Divorced Medical No 3
## 1303 Research & Development Married Medical No 4
## 1304 Research & Development Divorced Life Sciences No 3
## 1305 Research & Development Divorced Life Sciences No 3
## 1306 Research & Development Married Medical No 4
## 1307 Sales Married Marketing No 4
## 1308 Research & Development Married Medical No 3
## 1309 Sales Married Marketing No 4
## 1310 Sales Single Medical No 3
## 1311 Research & Development Married Life Sciences No 4
## 1312 Research & Development Single Medical No 3
## 1313 Human Resources Married Human Resources Yes 5
## 1314 Human Resources Divorced Human Resources Yes 3
## 1315 Sales Married Life Sciences No 4
## 1316 Research & Development Married Other No 4
## 1317 Sales Married Life Sciences No 4
## 1318 Research & Development Single Life Sciences No 2
## 1319 Research & Development Married Medical No 1
## 1320 Sales Single Marketing No 4
## 1321 Research & Development Married Technical Degree No 4
## 1322 Research & Development Single Life Sciences No 4
## 1323 Research & Development Divorced Life Sciences No 2
## 1324 Human Resources Divorced Life Sciences No 2
## 1325 Research & Development Divorced Life Sciences No 1
## 1326 Research & Development Single Life Sciences No 3
## 1327 Sales Single Marketing Yes 4
## 1328 Sales Divorced Technical Degree No 3
## 1329 Sales Married Medical No 1
## 1330 Human Resources Married Medical No 1
## 1331 Research & Development Married Medical No 3
## 1332 Research & Development Married Life Sciences No 3
## 1333 Research & Development Single Life Sciences Yes 2
## 1334 Sales Married Life Sciences Yes 3
## 1335 Research & Development Married Life Sciences No 3
## 1336 Research & Development Divorced Other No 4
## 1337 Research & Development Married Technical Degree No 4
## 1338 Sales Married Medical No 3
## 1339 Sales Single Medical Yes 3
## 1340 Research & Development Single Life Sciences Yes 1
## 1341 Sales Married Technical Degree No 4
## 1342 Research & Development Divorced Life Sciences No 3
## 1343 Sales Married Life Sciences No 3
## 1344 Research & Development Single Life Sciences No 3
## 1345 Research & Development Married Medical No 4
## 1346 Research & Development Married Other No 2
## 1347 Research & Development Married Life Sciences No 2
## 1348 Human Resources Single Human Resources No 1
## 1349 Research & Development Divorced Life Sciences No 4
## 1350 Research & Development Married Life Sciences No 2
## 1351 Sales Single Medical No 2
## 1352 Research & Development Divorced Medical No 3
## 1353 Research & Development Married Life Sciences No 4
## 1354 Research & Development Married Technical Degree Yes 4
## 1355 Research & Development Single Life Sciences Yes 2
## 1356 Sales Married Marketing No 2
## 1357 Sales Married Marketing No 3
## 1358 Research & Development Married Medical No 3
## 1359 Sales Divorced Medical No 2
## 1360 Sales Married Medical No 1
## 1361 Research & Development Divorced Medical No 3
## 1362 Research & Development Married Other No 3
## 1363 Research & Development Single Medical No 4
## 1364 Sales Single Marketing No 4
## 1365 Sales Married Life Sciences No 2
## 1366 Sales Single Technical Degree Yes 3
## 1367 Sales Married Life Sciences No 4
## 1368 Research & Development Married Technical Degree No 4
## 1369 Research & Development Married Other No 4
## 1370 Sales Single Marketing Yes 2
## 1371 Research & Development Married Technical Degree No 4
## 1372 Sales Married Marketing No 5
## 1373 Research & Development Married Medical No 2
## 1374 Research & Development Divorced Medical No 3
## 1375 Sales Married Life Sciences No 3
## 1376 Research & Development Single Life Sciences Yes 2
## 1377 Research & Development Divorced Life Sciences No 2
## 1378 Research & Development Married Life Sciences No 1
## 1379 Sales Divorced Marketing No 4
## 1380 Human Resources Married Human Resources Yes 3
## 1381 Sales Married Medical No 4
## 1382 Research & Development Single Medical No 3
## 1383 Research & Development Divorced Medical No 2
## 1384 Research & Development Married Life Sciences No 4
## 1385 Sales Single Marketing No 3
## 1386 Sales Divorced Medical No 4
## 1387 Research & Development Single Medical No 3
## 1388 Research & Development Married Life Sciences No 3
## 1389 Research & Development Divorced Medical No 4
## 1390 Research & Development Married Life Sciences No 3
## 1391 Research & Development Divorced Technical Degree Yes 3
## 1392 Sales Single Life Sciences No 3
## 1393 Sales Married Life Sciences No 4
## 1394 Sales Single Marketing No 3
## 1395 Research & Development Single Life Sciences No 4
## 1396 Sales Married Marketing Yes 4
## 1397 Sales Single Life Sciences Yes 4
## 1398 Research & Development Married Life Sciences No 2
## 1399 Research & Development Divorced Life Sciences No 2
## 1400 Research & Development Married Life Sciences No 3
## 1401 Human Resources Married Other No 4
## 1402 Human Resources Married Human Resources No 4
## 1403 Research & Development Divorced Medical No 1
## 1404 Sales Single Marketing No 4
## 1405 Research & Development Single Life Sciences No 2
## 1406 Research & Development Married Medical No 3
## 1407 Research & Development Single Medical No 3
## 1408 Research & Development Single Life Sciences No 2
## 1409 Research & Development Single Other No 2
## 1410 Research & Development Married Technical Degree No 3
## 1411 Sales Married Marketing No 2
## 1412 Human Resources Married Human Resources No 3
## 1413 Research & Development Married Medical No 2
## 1414 Research & Development Divorced Other No 1
## 1415 Research & Development Single Medical No 3
## 1416 Research & Development Divorced Medical No 2
## 1417 Sales Married Life Sciences No 4
## 1418 Sales Married Life Sciences No 2
## 1419 Research & Development Married Life Sciences No 4
## 1420 Research & Development Divorced Life Sciences No 4
## 1421 Research & Development Married Life Sciences No 3
## 1422 Research & Development Married Medical No 1
## 1423 Research & Development Married Medical No 4
## 1424 Research & Development Single Life Sciences No 2
## 1425 Research & Development Single Medical No 4
## 1426 Research & Development Married Medical No 2
## 1427 Research & Development Single Life Sciences No 4
## 1428 Research & Development Married Life Sciences No 4
## 1429 Sales Married Medical No 4
## 1430 Research & Development Single Life Sciences No 1
## 1431 Research & Development Married Medical No 3
## 1432 Sales Married Marketing No 4
## 1433 Research & Development Married Life Sciences No 3
## 1434 Sales Divorced Other No 2
## 1435 Sales Divorced Life Sciences No 4
## 1436 Research & Development Single Medical No 3
## 1437 Sales Single Medical No 1
## 1438 Research & Development Single Life Sciences No 3
## 1439 Sales Married Marketing Yes 3
## 1440 Sales Married Medical No 3
## 1441 Research & Development Divorced Life Sciences No 2
## 1442 Research & Development Divorced Life Sciences No 4
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## 1444 Research & Development Married Life Sciences No 3
## 1445 Research & Development Married Technical Degree Yes 2
## 1446 Research & Development Married Life Sciences No 4
## 1447 Sales Married Marketing No 3
## 1448 Sales Divorced Marketing No 4
## 1449 Sales Divorced Life Sciences No 3
## 1450 Research & Development Single Technical Degree No 3
## 1451 Human Resources Single Life Sciences No 4
## 1452 Sales Married Life Sciences No 2
## 1453 Sales Divorced Life Sciences Yes 4
## 1454 Sales Married Marketing No 4
## 1455 Sales Single Life Sciences No 3
## 1456 Research & Development Single Life Sciences No 4
## 1457 Research & Development Married Life Sciences No 4
## 1458 Research & Development Married Medical No 4
## 1459 Research & Development Married Life Sciences No 4
## 1460 Research & Development Married Other No 2
## 1461 Research & Development Single Medical No 4
## 1462 Sales Divorced Marketing Yes 3
## 1463 Sales Married Marketing No 1
## 1464 Research & Development Single Medical No 3
## 1465 Sales Single Other No 3
## 1466 Research & Development Married Medical No 2
## 1467 Research & Development Married Medical No 1
## 1468 Research & Development Married Life Sciences No 3
## 1469 Sales Married Medical No 3
## 1470 Research & Development Married Medical No 3
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head(attrition_data)
## Department MaritalStatus EducationField Attrition Education
## 1 Sales Single Life Sciences Yes 2
## 2 Research & Development Married Life Sciences No 1
## 3 Research & Development Single Other Yes 2
## 4 Research & Development Married Life Sciences No 4
## 5 Research & Development Married Medical No 1
## 6 Research & Development Single Life Sciences No 2
## DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age MonthlyIncome
## 1 1 2 4 41 5993
## 2 8 3 2 49 5130
## 3 2 4 3 37 2090
## 4 3 4 3 33 2909
## 5 2 1 2 27 3468
## 6 2 4 4 32 3068
## NumCompaniesWorked WorkLifeBalance YearsAtCompany
## 1 8 1 6
## 2 1 3 10
## 3 6 3 0
## 4 1 3 8
## 5 9 3 2
## 6 0 2 7
str(attrition_data)
## 'data.frame': 1470 obs. of 13 variables:
## $ Department : chr "Sales" "Research & Development" "Research & Development" "Research & Development" ...
## $ MaritalStatus : chr "Single" "Married" "Single" "Married" ...
## $ EducationField : chr "Life Sciences" "Life Sciences" "Other" "Life Sciences" ...
## $ Attrition : chr "Yes" "No" "Yes" "No" ...
## $ Education : int 2 1 2 4 1 2 3 1 3 3 ...
## $ DistanceFromHome : int 1 8 2 3 2 2 3 24 23 27 ...
## $ EnvironmentSatisfaction: int 2 3 4 4 1 4 3 4 4 3 ...
## $ JobSatisfaction : int 4 2 3 3 2 4 1 3 3 3 ...
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
#Converting necessary columns into Factors
attrition_data$Attrition <- as.factor(attrition_data$Attrition)
attrition_data$Education <- as.factor(attrition_data$Education)
attrition_data$JobSatisfaction <- as.factor(attrition_data$JobSatisfaction)
attrition_data$EnvironmentSatisfaction <- as.factor(attrition_data$EnvironmentSatisfaction)
attrition_data$WorkLifeBalance <- as.factor(attrition_data$WorkLifeBalance)
nrow(attrition_data)
## [1] 1470
## Exploratory Analysis
xtabs(~ Attrition + Education, data=attrition_data)
## Education
## Attrition 1 2 3 4 5
## No 139 238 473 340 43
## Yes 31 44 99 58 5
xtabs(~ Attrition + JobSatisfaction, data=attrition_data)
## JobSatisfaction
## Attrition 1 2 3 4
## No 223 234 369 407
## Yes 66 46 73 52
xtabs(~ Attrition + EnvironmentSatisfaction, data=attrition_data)
## EnvironmentSatisfaction
## Attrition 1 2 3 4
## No 212 244 391 386
## Yes 72 43 62 60
xtabs(~ Attrition + WorkLifeBalance, data=attrition_data)
## WorkLifeBalance
## Attrition 1 2 3 4
## No 55 286 766 126
## Yes 25 58 127 27
#Model Development
logistic_simple <- glm(Attrition ~ Education+JobSatisfaction+EnvironmentSatisfaction+WorkLifeBalance, data=attrition_data, family="binomial")
summary(logistic_simple)
##
## Call:
## glm(formula = Attrition ~ Education + JobSatisfaction + EnvironmentSatisfaction +
## WorkLifeBalance, family = "binomial", data = attrition_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.4331 0.3666 1.181 0.237417
## Education2 -0.2516 0.2629 -0.957 0.338485
## Education3 -0.1436 0.2325 -0.618 0.536755
## Education4 -0.3577 0.2496 -1.433 0.151752
## Education5 -0.7242 0.5195 -1.394 0.163266
## JobSatisfaction2 -0.4294 0.2176 -1.973 0.048489 *
## JobSatisfaction3 -0.4494 0.1939 -2.317 0.020490 *
## JobSatisfaction4 -0.8619 0.2067 -4.169 3.05e-05 ***
## EnvironmentSatisfaction2 -0.6427 0.2186 -2.940 0.003287 **
## EnvironmentSatisfaction3 -0.7754 0.1971 -3.934 8.35e-05 ***
## EnvironmentSatisfaction4 -0.7856 0.1983 -3.961 7.45e-05 ***
## WorkLifeBalance2 -0.7712 0.2886 -2.673 0.007529 **
## WorkLifeBalance3 -0.9864 0.2666 -3.700 0.000216 ***
## WorkLifeBalance4 -0.7186 0.3291 -2.184 0.028982 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1298.6 on 1469 degrees of freedom
## Residual deviance: 1243.5 on 1456 degrees of freedom
## AIC: 1271.5
##
## Number of Fisher Scoring iterations: 4
#Most of the predictor variables ("Education", "JobSatisfaction", etc.) have coefficients with statistically significant p-values (all p-values are greater than alpha). This suggests that there is insufficient evidence to conclude that any of these variables have a significant impact on Attrition.
predicted.attrition_data <- data.frame(probability.of.Attrition=logistic_simple$fitted.values,JobSatisfaction=attrition_data$JobSatisfaction)
predicted.attrition_data
## probability.of.Attrition JobSatisfaction
## 1 0.21030618 4
## 2 0.14703800 2
## 3 0.11506678 3
## 4 0.10469892 3
## 5 0.27236401 2
## 6 0.09645536 4
## 7 0.22147291 1
## 8 0.14327491 3
## 9 0.12652919 3
## 10 0.15361462 3
## 11 0.24484248 2
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## 13 0.31270240 3
## 14 0.09033978 4
## 15 0.12766776 3
## 16 0.17455487 1
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## 18 0.09645536 4
## 19 0.14518166 4
## 20 0.08750724 4
## 21 0.26131149 3
## 22 0.15625192 1
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## 25 0.23219394 1
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## 27 0.23219394 1
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## 1375 0.10628647 4
## 1376 0.22194381 3
## 1377 0.11489252 4
## 1378 0.11326204 4
## 1379 0.08199347 4
## 1380 0.24484248 2
## 1381 0.36186670 1
## 1382 0.15361462 3
## 1383 0.21206354 1
## 1384 0.20744743 2
## 1385 0.20691501 4
## 1386 0.12665543 3
## 1387 0.22147291 1
## 1388 0.38184110 1
## 1389 0.07254308 4
## 1390 0.18503844 1
## 1391 0.10726525 4
## 1392 0.38184110 1
## 1393 0.07254308 4
## 1394 0.08750724 4
## 1395 0.07185564 4
## 1396 0.14518166 4
## 1397 0.33274172 1
## 1398 0.26131149 3
## 1399 0.11506678 3
## 1400 0.24115153 3
## 1401 0.10659476 2
## 1402 0.10757604 2
## 1403 0.09967788 4
## 1404 0.17455487 1
## 1405 0.11506678 3
## 1406 0.16057474 3
## 1407 0.18659103 1
## 1408 0.15685397 3
## 1409 0.10113511 4
## 1410 0.15919626 3
## 1411 0.13273719 2
## 1412 0.12991915 2
## 1413 0.14127712 2
## 1414 0.17176915 3
## 1415 0.24115153 3
## 1416 0.15685397 3
## 1417 0.10659476 2
## 1418 0.22194381 3
## 1419 0.20416779 3
## 1420 0.18521067 1
## 1421 0.08750724 4
## 1422 0.31613059 2
## 1423 0.10469892 3
## 1424 0.14526667 3
## 1425 0.11887699 3
## 1426 0.09033978 4
## 1427 0.10757604 2
## 1428 0.17397810 4
## 1429 0.12099487 2
## 1430 0.19541773 4
## 1431 0.14319066 3
## 1432 0.07254308 4
## 1433 0.08833018 4
## 1434 0.26131149 3
## 1435 0.17397810 4
## 1436 0.09961629 4
## 1437 0.20938028 1
## 1438 0.10628647 4
## 1439 0.21970847 1
## 1440 0.17381408 4
## 1441 0.11712579 2
## 1442 0.12779496 3
## 1443 0.18166283 4
## 1444 0.28268836 3
## 1445 0.25853685 3
## 1446 0.20744743 2
## 1447 0.12652919 3
## 1448 0.08759845 4
## 1449 0.12991915 2
## 1450 0.18503844 1
## 1451 0.07254308 4
## 1452 0.15884708 4
## 1453 0.11887699 3
## 1454 0.09971874 4
## 1455 0.12652919 3
## 1456 0.10566481 3
## 1457 0.13377012 3
## 1458 0.10566481 3
## 1459 0.07254308 4
## 1460 0.11712579 2
## 1461 0.32954700 1
## 1462 0.18503844 1
## 1463 0.13674006 4
## 1464 0.20757354 1
## 1465 0.12652919 3
## 1466 0.08001127 4
## 1467 0.20768648 1
## 1468 0.14567009 2
## 1469 0.15489348 2
## 1470 0.17927647 3
xtabs(~ probability.of.Attrition + JobSatisfaction, data=predicted.attrition_data)
## JobSatisfaction
## probability.of.Attrition 1 2 3 4
## 0.0509290079067831 0 0 0 2
## 0.0514273436171294 0 0 0 4
## 0.0582998377960836 0 0 0 2
## 0.0623952334636104 0 0 0 2
## 0.0629983176993634 0 0 0 1
## 0.0713008702674125 0 0 0 1
## 0.0718556351495316 0 0 0 19
## 0.0725430845984081 0 0 0 21
## 0.0749799978493843 0 0 5 0
## 0.0756949005940833 0 0 1 0
## 0.077110782651787 0 2 0 0
## 0.0792590930438247 0 0 0 15
## 0.080011266146487 0 0 0 19
## 0.081993468100554 0 0 0 12
## 0.0855180198894394 0 0 3 0
## 0.087507237727187 0 0 0 34
## 0.0875984470468998 0 0 0 10
## 0.0883301769201772 0 0 0 35
## 0.0884221608764325 0 0 0 6
## 0.0903397835979433 0 0 0 9
## 0.0918921897522134 0 0 0 8
## 0.0927521744594639 0 0 0 3
## 0.0964553596809268 0 0 0 8
## 0.0973534712131155 0 0 0 5
## 0.098457260743169 0 1 0 0
## 0.0996162893638429 0 0 0 15
## 0.0996778826000728 0 0 0 6
## 0.0997187407399155 0 0 0 11
## 0.100602658695497 0 0 0 9
## 0.101135113194539 0 0 0 3
## 0.102071876199039 0 0 0 3
## 0.103918975399478 0 0 1 0
## 0.104538506138376 0 0 0 2
## 0.10469891785967 0 0 23 0
## 0.105323474886705 0 0 0 2
## 0.105664810160256 0 0 25 0
## 0.106286467128127 0 0 0 13
## 0.106594757383462 0 12 0 0
## 0.107265250546574 0 0 0 15
## 0.107576038089765 0 18 0 0
## 0.109653835581753 0 0 0 4
## 0.111384399895774 0 0 0 6
## 0.112404225208671 0 0 0 6
## 0.112728407991961 3 0 0 0
## 0.11326203772172 0 0 0 7
## 0.113758963576751 1 0 0 0
## 0.114892517602362 0 0 0 3
## 0.115066775691243 0 0 16 0
## 0.116115910875028 0 0 12 0
## 0.117125791387022 0 15 0 0
## 0.118191192539639 0 5 0 0
## 0.118876992593182 0 0 16 0
## 0.120650553018122 0 0 0 10
## 0.120723408053277 0 0 0 7
## 0.120994866523147 0 12 0 0
## 0.121817018613995 0 0 0 6
## 0.125797497861938 0 0 0 1
## 0.126340050931888 0 0 0 2
## 0.126415847673817 0 0 0 2
## 0.126529189520492 0 0 31 0
## 0.126655426204567 0 0 9 0
## 0.127667757177992 0 0 29 0
## 0.127794963602211 0 0 7 0
## 0.127838558252525 5 0 0 0
## 0.128763469974754 0 18 0 0
## 0.128891606840147 0 1 0 0
## 0.129919152303181 0 23 0 0
## 0.130048267559357 0 4 0 0
## 0.130444281026318 0 0 10 0
## 0.132585399361209 0 0 4 0
## 0.132737189137561 0 8 0 0
## 0.133770117545264 0 0 6 0
## 0.13611233527977 0 2 0 0
## 0.136740055060516 0 0 0 6
## 0.138860312712789 0 0 7 0
## 0.140092044919744 0 0 1 0
## 0.141277120194971 0 4 0 0
## 0.142413348775066 1 0 0 0
## 0.142526742043798 0 5 0 0
## 0.14306484214723 0 0 0 2
## 0.143190664405774 0 0 18 0
## 0.143274912664277 0 0 12 0
## 0.14333079632972 0 0 5 0
## 0.144539231016402 0 0 12 0
## 0.145181658301975 0 0 0 20
## 0.145266667381274 0 0 5 0
## 0.145670090677133 0 16 0 0
## 0.145755549577505 0 9 0 0
## 0.145812236126969 0 3 0 0
## 0.14654555537306 0 0 2 0
## 0.147038001148758 0 3 0 0
## 0.147775840916641 0 3 0 0
## 0.149072966283064 0 2 0 0
## 0.149907494334225 0 0 3 0
## 0.150975696617432 0 0 3 0
## 0.152285047846937 0 0 5 0
## 0.15356576449936 0 1 0 0
## 0.153614619077793 0 0 14 0
## 0.153814012517148 2 0 0 0
## 0.154893480328818 0 16 0 0
## 0.154903696838202 16 0 0 0
## 0.156241627873186 0 7 0 0
## 0.156251916863363 13 0 0 0
## 0.156853970839863 0 0 9 0
## 0.158847080347473 0 0 0 13
## 0.159196257994002 0 0 2 0
## 0.159525935547074 0 1 0 0
## 0.160574739934627 0 0 11 0
## 0.16173318099462 0 0 8 0
## 0.161900461305183 0 5 0 0
## 0.163297811252923 0 5 0 0
## 0.16447204832165 0 3 0 0
## 0.169302976820758 8 0 0 0
## 0.1707512004779 9 0 0 0
## 0.171671502508262 0 0 3 0
## 0.171769148485401 0 0 4 0
## 0.17323406854789 0 0 4 0
## 0.173380866518913 0 0 0 2
## 0.173814080718024 0 0 0 12
## 0.173978096540129 0 0 0 9
## 0.174543626710983 0 8 0 0
## 0.174554871605932 6 0 0 0
## 0.176126776416665 0 2 0 0
## 0.178553046391665 0 0 1 0
## 0.179276468779857 0 0 2 0
## 0.180678461133255 0 0 1 0
## 0.180893139056416 0 0 1 0
## 0.181662834254414 0 0 0 5
## 0.182247832910883 0 3 0 0
## 0.182350170331644 0 1 0 0
## 0.183885294709649 0 1 0 0
## 0.185038437559028 29 0 0 0
## 0.185210670616467 3 0 0 0
## 0.186591028695308 26 0 0 0
## 0.186764375715122 6 0 0 0
## 0.18754462338252 0 0 0 2
## 0.189113363320436 0 0 0 3
## 0.189752345724027 0 0 0 3
## 0.190369363648409 10 0 0 0
## 0.191681283849845 0 1 0 0
## 0.193071079336448 0 0 2 0
## 0.193275468107813 2 0 0 0
## 0.194880646083123 2 0 0 0
## 0.195417729603417 0 0 0 7
## 0.197966855825351 0 0 0 1
## 0.201393549310678 0 0 2 0
## 0.201754603760539 1 0 0 0
## 0.203412445852437 6 0 0 0
## 0.204167785672997 0 0 12 0
## 0.204558013968573 0 0 0 3
## 0.206232940501757 0 0 0 6
## 0.206915006914568 0 0 0 5
## 0.207447425736185 0 9 0 0
## 0.207573535534971 7 0 0 0
## 0.207686482298745 4 0 0 0
## 0.207761396785367 2 0 0 0
## 0.209380282045724 11 0 0 0
## 0.210306176177526 0 0 0 2
## 0.210353806698662 1 0 0 0
## 0.212063537618124 3 0 0 0
## 0.215674730376081 0 0 0 1
## 0.216547168400016 3 0 0 0
## 0.217968471836822 1 0 0 0
## 0.219708474225798 8 0 0 0
## 0.221472913544375 9 0 0 0
## 0.221943805378288 0 0 10 0
## 0.225428106217822 0 5 0 0
## 0.225761539047481 2 0 0 0
## 0.228802914405725 0 0 0 1
## 0.228853520077302 1 0 0 0
## 0.228924075570263 0 0 0 1
## 0.230669690636481 2 0 0 0
## 0.231480121342915 0 0 0 2
## 0.232193941700538 4 0 0 0
## 0.238729264406724 0 0 1 0
## 0.240599355719945 0 0 1 0
## 0.240963833619512 0 0 0 1
## 0.241151526282332 0 0 21 0
## 0.241360520697161 0 0 6 0
## 0.244284577496501 0 2 0 0
## 0.244842478735896 0 13 0 0
## 0.24505363894791 0 2 0 0
## 0.245195537324504 7 0 0 0
## 0.245322617743932 1 0 0 0
## 0.247227584838395 2 0 0 0
## 0.251116762211551 0 0 6 0
## 0.25490900297663 0 1 0 0
## 0.255185142811261 1 0 0 0
## 0.257140599498429 3 0 0 0
## 0.258536851336972 0 0 1 0
## 0.260509008561369 0 0 1 0
## 0.26131148629305 0 0 6 0
## 0.262401883726328 0 1 0 0
## 0.264393010843622 0 1 0 0
## 0.265203162169218 0 2 0 0
## 0.268405639768603 0 0 6 0
## 0.269604466715346 0 1 0 0
## 0.271585479947482 0 0 1 0
## 0.27236401254192 0 3 0 0
## 0.272742423350016 1 0 0 0
## 0.27557308381707 0 1 0 0
## 0.279772707428973 0 0 4 0
## 0.28184527909725 0 0 1 0
## 0.282688356682348 0 0 13 0
## 0.283293487042157 3 0 0 0
## 0.283833680613878 0 2 0 0
## 0.285924393126101 0 2 0 0
## 0.286774800045495 0 2 0 0
## 0.286790763289162 9 0 0 0
## 0.286872186706422 0 0 1 0
## 0.293468918441472 0 0 2 0
## 0.297646536419118 0 3 0 0
## 0.308967615390497 6 0 0 0
## 0.309464071629478 0 0 1 0
## 0.312702396008166 0 0 4 0
## 0.312922647133924 0 0 0 2
## 0.313768266405902 0 4 0 0
## 0.316130592218064 0 2 0 0
## 0.317030952739893 0 1 0 0
## 0.329546998836545 5 0 0 0
## 0.331818422000885 1 0 0 0
## 0.332488280563482 14 0 0 0
## 0.332741723118045 2 0 0 0
## 0.35669476567226 1 0 0 0
## 0.360678321003082 0 0 0 1
## 0.361866697123994 2 0 0 0
## 0.368846380965801 3 0 0 0
## 0.37844232476821 2 0 0 0
## 0.381841095606331 7 0 0 0
## 0.38670128793995 1 0 0 0
## 0.394324269994077 4 0 0 0
## 0.407566651971291 0 0 3 0
## 0.412772631671937 1 0 0 0
## 0.41627323221199 1 0 0 0
## 0.433407445425862 0 0 1 0
## 0.438341225640952 0 1 0 0
## 0.460093985847148 0 0 4 0
## 0.465082193165234 0 1 0 0
## 0.495921480786214 0 0 1 0
## 0.500937723556929 0 1 0 0
## 0.518838682201947 2 0 0 0
## 0.545241455977253 1 0 0 0
## 0.571863931081163 2 0 0 0
logistic <- glm(Attrition ~ ., data=attrition_data, family="binomial")
summary(logistic)
##
## Call:
## glm(formula = Attrition ~ ., family = "binomial", data = attrition_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.081e+00 7.034e-01 2.959 0.003086 **
## DepartmentResearch & Development -1.083e-01 5.367e-01 -0.202 0.840158
## DepartmentSales 3.994e-01 5.521e-01 0.723 0.469419
## MaritalStatusMarried 2.797e-01 2.305e-01 1.214 0.224852
## MaritalStatusSingle 1.152e+00 2.283e-01 5.046 4.52e-07 ***
## EducationFieldLife Sciences -1.050e+00 7.253e-01 -1.447 0.147857
## EducationFieldMarketing -6.236e-01 7.643e-01 -0.816 0.414508
## EducationFieldMedical -1.195e+00 7.282e-01 -1.641 0.100808
## EducationFieldOther -1.094e+00 7.900e-01 -1.385 0.166159
## EducationFieldTechnical Degree -4.425e-01 7.411e-01 -0.597 0.550448
## Education2 -7.608e-03 2.866e-01 -0.027 0.978824
## Education3 1.119e-02 2.531e-01 0.044 0.964723
## Education4 -7.320e-02 2.794e-01 -0.262 0.793309
## Education5 -3.277e-01 5.462e-01 -0.600 0.548546
## DistanceFromHome 3.262e-02 9.159e-03 3.561 0.000369 ***
## EnvironmentSatisfaction2 -6.947e-01 2.330e-01 -2.982 0.002867 **
## EnvironmentSatisfaction3 -8.730e-01 2.132e-01 -4.094 4.24e-05 ***
## EnvironmentSatisfaction4 -8.957e-01 2.146e-01 -4.174 2.99e-05 ***
## JobSatisfaction2 -5.291e-01 2.353e-01 -2.249 0.024538 *
## JobSatisfaction3 -4.733e-01 2.081e-01 -2.275 0.022913 *
## JobSatisfaction4 -9.747e-01 2.213e-01 -4.404 1.06e-05 ***
## Age -3.526e-02 1.085e-02 -3.249 0.001159 **
## MonthlyIncome -1.042e-04 2.882e-05 -3.616 0.000300 ***
## NumCompaniesWorked 1.115e-01 3.224e-02 3.458 0.000544 ***
## WorkLifeBalance2 -7.698e-01 3.114e-01 -2.472 0.013439 *
## WorkLifeBalance3 -1.082e+00 2.877e-01 -3.762 0.000169 ***
## WorkLifeBalance4 -7.668e-01 3.549e-01 -2.161 0.030715 *
## YearsAtCompany -2.176e-02 1.951e-02 -1.116 0.264531
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1298.6 on 1469 degrees of freedom
## Residual deviance: 1095.2 on 1442 degrees of freedom
## AIC: 1151.2
##
## Number of Fisher Scoring iterations: 5
## Now calculate the overall "Pseudo R-squared" and its p-value
ll.null <- logistic$null.deviance/-2
ll.proposed <- logistic$deviance/-2
(ll.null - ll.proposed) / ll.null
## [1] 0.1566413
## The p-value for the R^2
1 - pchisq(2*(ll.proposed - ll.null), df=(length(logistic$coefficients)-1))
## [1] 0
predicted.attrition_data <- data.frame(probability.of.Attrition=logistic$fitted.values,Attrition=attrition_data$Attrition)
predicted.attrition_data <- predicted.attrition_data[order(predicted.attrition_data$probability.of.Attrition, decreasing=FALSE),]
predicted.attrition_data$rank <- 1:nrow(predicted.attrition_data)
# The Pseudo R-squared measures the proportion of total variance in the response variable that is explained by the model.
# The output of 0.2 indicates that the model does not fits the data perfectly.
# As the p-value for R^2 is less than 0.05, we reject the null hypothesis.
plot(logistic)
# Residuals vs Fitted are a great way to identify heteroscedasticity via pattern recognition, however our model does not seem to have any.
# Q-Q Plots are great in understanding the distribution of residuals. As it can be observed that there is quite some deviation from the straight line indicating that residuals do not follow a normal distribution.
# Scale-Location Plot shows the square root of the standardized residuals against the fitted values. As it may be observed that the spread of points is not consistent across the range of fitted values, it indicates that the variability of the residuals do not remain constant.
# Residuals Vs Leverage help in identifying potential problems with the regression model. Points on the right of the plot have a great influence on the model's parameters. Points with a Cook's Distance greater than highlighted threshold have a greater influence on the model.
ggplot(data=predicted.attrition_data, aes(x=rank, y=probability.of.Attrition)) +
geom_point(aes(color=Attrition), alpha=1, shape=4, stroke=2) +
xlab("Index") +
ylab("Predicted probability of Attrition")
# This plot highlights the performace of our model.
# It can be clearly inferred that the model performs poorly.
# From Caret
pdata <- predict(logistic,newdata=attrition_data,type="response" )
pdata
## 1 2 3 4 5 6
## 0.408492594 0.032649514 0.228672082 0.059930466 0.301137938 0.108368355
## 7 8 9 10 11 12
## 0.082374800 0.119863740 0.105012483 0.187685441 0.165726881 0.175172192
## 13 14 15 16 17 18
## 0.296189944 0.053094561 0.428664934 0.082384687 0.139115721 0.087880197
## 19 20 21 22 23 24
## 0.015495948 0.113102159 0.203580914 0.473883971 0.110025185 0.244133387
## 25 26 27 28 29 30
## 0.264553173 0.008327191 0.305253338 0.072575521 0.026398205 0.145700592
## 31 32 33 34 35 36
## 0.127543427 0.035073559 0.163975540 0.193892777 0.095917807 0.043424939
## 37 38 39 40 41 42
## 0.209999348 0.107605383 0.307334036 0.140607893 0.036419116 0.102597279
## 43 44 45 46 47 48
## 0.644033005 0.176304832 0.069126258 0.020096006 0.392977382 0.156280961
## 49 50 51 52 53 54
## 0.282663362 0.053687109 0.325927834 0.349431255 0.174793881 0.064501850
## 55 56 57 58 59 60
## 0.417620313 0.060807986 0.147049886 0.170520433 0.043560479 0.088887818
## 61 62 63 64 65 66
## 0.056778525 0.123927652 0.009147970 0.521737381 0.038951666 0.008461105
## 67 68 69 70 71 72
## 0.138691420 0.046852899 0.190759758 0.081620697 0.357831981 0.068003759
## 73 74 75 76 77 78
## 0.134856545 0.050131943 0.068187639 0.087171911 0.269626516 0.052051514
## 79 80 81 82 83 84
## 0.175635763 0.068843818 0.042998971 0.138553093 0.046765229 0.040527797
## 85 86 87 88 89 90
## 0.101983405 0.060594949 0.361177512 0.035698745 0.036659502 0.051423682
## 91 92 93 94 95 96
## 0.014859223 0.307933405 0.076429002 0.036612310 0.187217492 0.255271578
## 97 98 99 100 101 102
## 0.285200076 0.160811997 0.023113873 0.174347534 0.290812115 0.228568070
## 103 104 105 106 107 108
## 0.169300905 0.207768713 0.050187664 0.024535768 0.027969995 0.322085585
## 109 110 111 112 113 114
## 0.058353621 0.216796791 0.196718820 0.239273035 0.079032956 0.153928768
## 115 116 117 118 119 120
## 0.078743592 0.099551556 0.092960489 0.071592030 0.111806198 0.022328250
## 121 122 123 124 125 126
## 0.269992245 0.217792142 0.089748993 0.059408490 0.175489165 0.122709904
## 127 128 129 130 131 132
## 0.008291107 0.701580372 0.105593171 0.067043063 0.264053071 0.137251795
## 133 134 135 136 137 138
## 0.239917367 0.053946622 0.169708093 0.074435612 0.071370097 0.096348346
## 139 140 141 142 143 144
## 0.372251360 0.242208371 0.639596441 0.222699094 0.179607855 0.525274180
## 145 146 147 148 149 150
## 0.054452384 0.236381021 0.099188010 0.033988481 0.109438004 0.266445447
## 151 152 153 154 155 156
## 0.048017431 0.060481776 0.292825953 0.213286787 0.165114568 0.100918714
## 157 158 159 160 161 162
## 0.036495892 0.069088231 0.079742338 0.240635964 0.099546520 0.293259135
## 163 164 165 166 167 168
## 0.204044730 0.051319938 0.086373404 0.025270515 0.165850767 0.052128591
## 169 170 171 172 173 174
## 0.236464640 0.153905326 0.235856163 0.661697693 0.199504713 0.083173107
## 175 176 177 178 179 180
## 0.135033081 0.058664172 0.124333994 0.272415949 0.046670105 0.111169431
## 181 182 183 184 185 186
## 0.101703703 0.271737638 0.477948942 0.047225123 0.043457997 0.076223514
## 187 188 189 190 191 192
## 0.006824491 0.024331133 0.040298496 0.028886522 0.002727602 0.233236339
## 193 194 195 196 197 198
## 0.136765101 0.046688133 0.023894715 0.213497357 0.172532214 0.052723048
## 199 200 201 202 203 204
## 0.091355067 0.286310356 0.269270779 0.018111284 0.063060600 0.129969309
## 205 206 207 208 209 210
## 0.259242503 0.208270044 0.109991017 0.142982369 0.156832319 0.041164175
## 211 212 213 214 215 216
## 0.031590470 0.084007856 0.224880457 0.069591120 0.481932775 0.062283301
## 217 218 219 220 221 222
## 0.692613582 0.319234127 0.071558117 0.103146660 0.224898959 0.099528991
## 223 224 225 226 227 228
## 0.015024796 0.076093985 0.044533926 0.026279814 0.184188605 0.041923375
## 229 230 231 232 233 234
## 0.211442273 0.206293750 0.130439607 0.007775105 0.113844970 0.006628429
## 235 236 237 238 239 240
## 0.215678497 0.036074117 0.409199673 0.043433756 0.113779511 0.303215643
## 241 242 243 244 245 246
## 0.070196131 0.157462579 0.158161648 0.169119814 0.002908839 0.047170223
## 247 248 249 250 251 252
## 0.061597600 0.102217020 0.107597451 0.111668426 0.104835892 0.064029845
## 253 254 255 256 257 258
## 0.162536656 0.222815597 0.115277538 0.143378429 0.044344284 0.009829489
## 259 260 261 262 263 264
## 0.033472691 0.296307649 0.231825947 0.051625846 0.432966495 0.048541911
## 265 266 267 268 269 270
## 0.614601253 0.188262316 0.057158009 0.117593710 0.009417524 0.030092747
## 271 272 273 274 275 276
## 0.008913491 0.097855453 0.077408756 0.070983879 0.241171971 0.019315141
## 277 278 279 280 281 282
## 0.099967987 0.173307397 0.115336863 0.020112101 0.010887560 0.056101556
## 283 284 285 286 287 288
## 0.197541283 0.063957348 0.253242651 0.068063552 0.227962665 0.088589867
## 289 290 291 292 293 294
## 0.199255607 0.124191582 0.086165931 0.239119437 0.185571464 0.186507812
## 295 296 297 298 299 300
## 0.069179774 0.125530093 0.285953799 0.140475644 0.079993508 0.027877388
## 301 302 303 304 305 306
## 0.031874492 0.419634385 0.252791454 0.193860205 0.010310030 0.158501737
## 307 308 309 310 311 312
## 0.113066413 0.111030700 0.016477763 0.060995615 0.471313424 0.078728003
## 313 314 315 316 317 318
## 0.087085823 0.040542810 0.016783049 0.072587849 0.093159672 0.038197955
## 319 320 321 322 323 324
## 0.248244764 0.147091095 0.230128332 0.080031035 0.299548325 0.174954917
## 325 326 327 328 329 330
## 0.059808637 0.041656003 0.004585408 0.121319039 0.363052092 0.009989507
## 331 332 333 334 335 336
## 0.043723996 0.115341029 0.161337208 0.131609074 0.057744309 0.052134877
## 337 338 339 340 341 342
## 0.197474419 0.094715169 0.097852915 0.161969938 0.046400010 0.013340553
## 343 344 345 346 347 348
## 0.076026098 0.095461857 0.105495098 0.126162587 0.131919108 0.211676595
## 349 350 351 352 353 354
## 0.075501240 0.137737610 0.072317041 0.057975772 0.349078571 0.068894444
## 355 356 357 358 359 360
## 0.543736169 0.099288951 0.129153319 0.666145547 0.087196098 0.070184028
## 361 362 363 364 365 366
## 0.018162322 0.079143039 0.503227775 0.345534384 0.159178485 0.053710721
## 367 368 369 370 371 372
## 0.280173860 0.099077864 0.172981224 0.167713636 0.393574254 0.394216374
## 373 374 375 376 377 378
## 0.245552379 0.045178904 0.178926388 0.112374765 0.077496110 0.090824146
## 379 380 381 382 383 384
## 0.716453324 0.012880788 0.211938896 0.209615484 0.366957219 0.245056032
## 385 386 387 388 389 390
## 0.057639518 0.396525043 0.101982703 0.127119330 0.081824179 0.200322398
## 391 392 393 394 395 396
## 0.023478141 0.096338869 0.042130216 0.235674296 0.244256903 0.096638807
## 397 398 399 400 401 402
## 0.046892066 0.199089944 0.081550398 0.114099865 0.006592622 0.097481934
## 403 404 405 406 407 408
## 0.375362185 0.116850315 0.099870357 0.331135768 0.021161859 0.142424167
## 409 410 411 412 413 414
## 0.018182756 0.177203510 0.086563420 0.058107089 0.054284628 0.112067992
## 415 416 417 418 419 420
## 0.606917844 0.170643922 0.042313938 0.011529497 0.386671824 0.186210497
## 421 422 423 424 425 426
## 0.028192698 0.344124446 0.564529758 0.144980639 0.109215599 0.013370111
## 427 428 429 430 431 432
## 0.101983290 0.153184891 0.049350421 0.111716539 0.192994265 0.153859290
## 433 434 435 436 437 438
## 0.055151885 0.053894921 0.034689881 0.087739873 0.144537701 0.331045866
## 439 440 441 442 443 444
## 0.077802330 0.183480375 0.442290803 0.096872179 0.103033425 0.429719853
## 445 446 447 448 449 450
## 0.049038492 0.087421391 0.158412544 0.262830068 0.082230263 0.057675223
## 451 452 453 454 455 456
## 0.222451990 0.102234999 0.062376403 0.144345021 0.173385540 0.026412491
## 457 458 459 460 461 462
## 0.087081332 0.539555645 0.132297941 0.162636714 0.465155177 0.307536808
## 463 464 465 466 467 468
## 0.165361157 0.635977086 0.185479715 0.141442914 0.042498550 0.082052793
## 469 470 471 472 473 474
## 0.071948309 0.211971853 0.150194811 0.043761305 0.093703638 0.004787429
## 475 476 477 478 479 480
## 0.110880387 0.544583589 0.144378543 0.010144281 0.197571389 0.217728320
## 481 482 483 484 485 486
## 0.351485453 0.042336244 0.393000222 0.388190983 0.154233951 0.163645694
## 487 488 489 490 491 492
## 0.135850314 0.272238149 0.023023580 0.013896009 0.307226508 0.025211333
## 493 494 495 496 497 498
## 0.089844353 0.295317973 0.189585331 0.199590115 0.604888907 0.009603225
## 499 500 501 502 503 504
## 0.196196588 0.083450655 0.106469490 0.061425710 0.188688781 0.042424864
## 505 506 507 508 509 510
## 0.394414351 0.064915414 0.027804267 0.129735410 0.060725265 0.066951560
## 511 512 513 514 515 516
## 0.030740570 0.036419582 0.205168278 0.285874856 0.373720708 0.083614094
## 517 518 519 520 521 522
## 0.374147324 0.121707105 0.154423551 0.036231967 0.086931534 0.046336473
## 523 524 525 526 527 528
## 0.115251709 0.052022486 0.107501664 0.680161620 0.124564313 0.251519185
## 529 530 531 532 533 534
## 0.129795329 0.060958850 0.073385208 0.053495793 0.334298169 0.074917220
## 535 536 537 538 539 540
## 0.015176858 0.024897146 0.632982499 0.085002374 0.020656210 0.166245615
## 541 542 543 544 545 546
## 0.474779056 0.219664469 0.150756424 0.341839702 0.035173942 0.229374470
## 547 548 549 550 551 552
## 0.328244596 0.103156911 0.064423354 0.157101552 0.239163210 0.464114819
## 553 554 555 556 557 558
## 0.021375960 0.084214965 0.587025042 0.181455685 0.068184850 0.090241085
## 559 560 561 562 563 564
## 0.126537107 0.170077366 0.089618739 0.024201514 0.099821613 0.293937119
## 565 566 567 568 569 570
## 0.189358946 0.399522944 0.314154848 0.098949223 0.012083599 0.382856406
## 571 572 573 574 575 576
## 0.023830889 0.100735318 0.233129772 0.712374508 0.107031833 0.096698879
## 577 578 579 580 581 582
## 0.116733076 0.107231148 0.346316744 0.153491383 0.213822474 0.085445728
## 583 584 585 586 587 588
## 0.036118229 0.201787729 0.006331127 0.195994107 0.091672321 0.087770058
## 589 590 591 592 593 594
## 0.011832989 0.151453725 0.029870175 0.774470790 0.005177597 0.035861016
## 595 596 597 598 599 600
## 0.130916009 0.012317928 0.165120748 0.051134256 0.266488218 0.300759558
## 601 602 603 604 605 606
## 0.045332361 0.384422802 0.138478252 0.137970975 0.134602314 0.213644751
## 607 608 609 610 611 612
## 0.133773926 0.061946709 0.087742454 0.054831018 0.026409102 0.121195815
## 613 614 615 616 617 618
## 0.151219262 0.259208825 0.080085590 0.076437142 0.114923918 0.198130802
## 619 620 621 622 623 624
## 0.663858072 0.194454005 0.412903455 0.052189156 0.106177227 0.121192969
## 625 626 627 628 629 630
## 0.115469235 0.100922513 0.116700253 0.013848714 0.156306749 0.042658715
## 631 632 633 634 635 636
## 0.215811021 0.114945130 0.120748177 0.245832420 0.181435118 0.027940883
## 637 638 639 640 641 642
## 0.111053441 0.031672297 0.332940332 0.112441059 0.155047203 0.086745760
## 643 644 645 646 647 648
## 0.175087084 0.038520004 0.069226706 0.163641599 0.096538155 0.100757466
## 649 650 651 652 653 654
## 0.135518481 0.041142106 0.041012237 0.046624612 0.316801972 0.012608905
## 655 656 657 658 659 660
## 0.063020605 0.236211585 0.625516966 0.147404747 0.102605742 0.268249716
## 661 662 663 664 665 666
## 0.049116375 0.155911098 0.388846799 0.278227832 0.036908665 0.117180933
## 667 668 669 670 671 672
## 0.129038337 0.049013173 0.112366548 0.372872170 0.242892135 0.085990577
## 673 674 675 676 677 678
## 0.268604412 0.240378313 0.021212257 0.227477355 0.149191329 0.075449303
## 679 680 681 682 683 684
## 0.120896199 0.221462196 0.097117518 0.043358233 0.118669051 0.314608345
## 685 686 687 688 689 690
## 0.196322723 0.293457942 0.124853461 0.138041650 0.560256379 0.693559538
## 691 692 693 694 695 696
## 0.090368485 0.081225404 0.079503107 0.024050170 0.067307864 0.276766461
## 697 698 699 700 701 702
## 0.048315228 0.240556839 0.121779412 0.006690702 0.172013603 0.020089269
## 703 704 705 706 707 708
## 0.129612673 0.209173008 0.043317467 0.167254348 0.273364461 0.033128054
## 709 710 711 712 713 714
## 0.208162934 0.242442726 0.083954612 0.457797560 0.181493974 0.021609633
## 715 716 717 718 719 720
## 0.010785726 0.042268886 0.021983079 0.375071365 0.110866407 0.081507396
## 721 722 723 724 725 726
## 0.362038786 0.026600791 0.083528340 0.023900072 0.083435336 0.149407960
## 727 728 729 730 731 732
## 0.097939367 0.239877445 0.083061216 0.041123078 0.080944152 0.362581356
## 733 734 735 736 737 738
## 0.171215367 0.032711224 0.267526509 0.226527398 0.064137831 0.162195548
## 739 740 741 742 743 744
## 0.008448412 0.089516936 0.056315964 0.070138047 0.105650462 0.016906522
## 745 746 747 748 749 750
## 0.404442161 0.033667422 0.006889242 0.209399321 0.733592218 0.012852644
## 751 752 753 754 755 756
## 0.034593303 0.028951560 0.223608001 0.102163121 0.259923040 0.020581033
## 757 758 759 760 761 762
## 0.409285955 0.040642771 0.079916900 0.199295665 0.046198239 0.293584503
## 763 764 765 766 767 768
## 0.418577429 0.141213637 0.164846968 0.069921881 0.009885763 0.176603662
## 769 770 771 772 773 774
## 0.274271084 0.133766634 0.007228760 0.036606027 0.086271384 0.041347440
## 775 776 777 778 779 780
## 0.060354464 0.051011883 0.373314182 0.492922359 0.081211009 0.222905253
## 781 782 783 784 785 786
## 0.497740116 0.209881068 0.114419490 0.106894586 0.046029607 0.124879350
## 787 788 789 790 791 792
## 0.141058247 0.017081585 0.278316311 0.065284308 0.032936580 0.258723043
## 793 794 795 796 797 798
## 0.364127468 0.262894777 0.153311857 0.044380967 0.118837237 0.300750063
## 799 800 801 802 803 804
## 0.535740605 0.009350620 0.123738097 0.133067383 0.096750189 0.053303404
## 805 806 807 808 809 810
## 0.039437410 0.062762114 0.083857447 0.060471938 0.103641011 0.035973284
## 811 812 813 814 815 816
## 0.063598895 0.312709664 0.143540721 0.035174498 0.029472060 0.409856027
## 817 818 819 820 821 822
## 0.273077941 0.173081671 0.120991782 0.333931050 0.076314896 0.067659233
## 823 824 825 826 827 828
## 0.187374390 0.079313991 0.203208789 0.058628602 0.200136134 0.074402466
## 829 830 831 832 833 834
## 0.277075894 0.504479877 0.054169873 0.135280899 0.069389924 0.096795322
## 835 836 837 838 839 840
## 0.148437516 0.487587794 0.413453788 0.119961471 0.116222640 0.558866540
## 841 842 843 844 845 846
## 0.082517180 0.450382568 0.101313548 0.082076642 0.141392703 0.181215732
## 847 848 849 850 851 852
## 0.032197837 0.114817384 0.055471084 0.690451684 0.142815676 0.016212419
## 853 854 855 856 857 858
## 0.049590362 0.391762350 0.165410692 0.027497445 0.497020298 0.121686115
## 859 860 861 862 863 864
## 0.006194479 0.108688872 0.058681795 0.056551631 0.201462756 0.206061677
## 865 866 867 868 869 870
## 0.515168333 0.417438066 0.113807334 0.013547894 0.152769246 0.018667747
## 871 872 873 874 875 876
## 0.148116866 0.340362715 0.216093985 0.048408835 0.071400523 0.083392426
## 877 878 879 880 881 882
## 0.464822611 0.031793144 0.099736015 0.025620108 0.096529158 0.155069865
## 883 884 885 886 887 888
## 0.066121512 0.079256959 0.255798355 0.171056103 0.044127677 0.114363410
## 889 890 891 892 893 894
## 0.084719067 0.408961768 0.056622367 0.065635294 0.549249360 0.078866134
## 895 896 897 898 899 900
## 0.005065190 0.113236345 0.242297591 0.080904594 0.006492971 0.028311368
## 901 902 903 904 905 906
## 0.115611484 0.293609127 0.151757902 0.029347495 0.030279770 0.014867424
## 907 908 909 910 911 912
## 0.243720100 0.041382943 0.055811465 0.322625656 0.111871493 0.384074926
## 913 914 915 916 917 918
## 0.154701096 0.085234121 0.004369332 0.726044311 0.020967553 0.352827145
## 919 920 921 922 923 924
## 0.010874390 0.052204159 0.098379017 0.175363751 0.010148211 0.127192288
## 925 926 927 928 929 930
## 0.063303150 0.102100577 0.093156046 0.168717028 0.047986394 0.047636978
## 931 932 933 934 935 936
## 0.112445864 0.239907778 0.158622214 0.503633142 0.222243748 0.065468989
## 937 938 939 940 941 942
## 0.063954318 0.013933762 0.101606251 0.058929933 0.239670293 0.144847678
## 943 944 945 946 947 948
## 0.098459820 0.285793387 0.027610246 0.047804484 0.269033835 0.245891192
## 949 950 951 952 953 954
## 0.067754508 0.284496270 0.050136937 0.107495098 0.299137154 0.294910619
## 955 956 957 958 959 960
## 0.009707200 0.005261863 0.025380178 0.135370163 0.024303038 0.059609266
## 961 962 963 964 965 966
## 0.106841334 0.113347347 0.005795469 0.103005924 0.339921171 0.123741153
## 967 968 969 970 971 972
## 0.049490377 0.072076673 0.437857587 0.033663570 0.207425828 0.108813279
## 973 974 975 976 977 978
## 0.229879734 0.021044761 0.170684089 0.270080827 0.020209337 0.357878363
## 979 980 981 982 983 984
## 0.039712846 0.150827100 0.359015222 0.215824333 0.053367025 0.116219595
## 985 986 987 988 989 990
## 0.296899001 0.092807596 0.230353379 0.054203337 0.057344766 0.112849622
## 991 992 993 994 995 996
## 0.099060430 0.169594092 0.061412076 0.421032103 0.036431173 0.353984819
## 997 998 999 1000 1001 1002
## 0.113977353 0.238931429 0.186614964 0.051002925 0.315855756 0.364114719
## 1003 1004 1005 1006 1007 1008
## 0.090697216 0.325665649 0.244834300 0.327299292 0.493027915 0.081234151
## 1009 1010 1011 1012 1013 1014
## 0.015637178 0.007878551 0.006044417 0.357087948 0.298887904 0.308652160
## 1015 1016 1017 1018 1019 1020
## 0.139157041 0.101563451 0.479242424 0.235194954 0.168994602 0.369440080
## 1021 1022 1023 1024 1025 1026
## 0.221945948 0.460993178 0.423560162 0.172081627 0.023261516 0.115826379
## 1027 1028 1029 1030 1031 1032
## 0.088553643 0.114942193 0.070689757 0.064290873 0.059430025 0.123447734
## 1033 1034 1035 1036 1037 1038
## 0.457898108 0.064224844 0.048240355 0.356621948 0.223485677 0.135585915
## 1039 1040 1041 1042 1043 1044
## 0.151819565 0.302950183 0.013589228 0.206891812 0.137755106 0.028295652
## 1045 1046 1047 1048 1049 1050
## 0.167118435 0.059763001 0.204105277 0.132471106 0.274253727 0.338923079
## 1051 1052 1053 1054 1055 1056
## 0.135380111 0.333765763 0.190469995 0.029559300 0.016893829 0.064082077
## 1057 1058 1059 1060 1061 1062
## 0.525059081 0.872322031 0.461800884 0.129316388 0.454257809 0.206166747
## 1063 1064 1065 1066 1067 1068
## 0.114675877 0.083673285 0.081708627 0.026188292 0.218103656 0.119945163
## 1069 1070 1071 1072 1073 1074
## 0.467827238 0.362025901 0.327995570 0.065782711 0.065508126 0.147378083
## 1075 1076 1077 1078 1079 1080
## 0.114178899 0.073586862 0.005310038 0.863695062 0.052717346 0.133640523
## 1081 1082 1083 1084 1085 1086
## 0.043417005 0.254438103 0.509376618 0.501250334 0.105975270 0.322130476
## 1087 1088 1089 1090 1091 1092
## 0.011435312 0.199353702 0.051597185 0.081566315 0.084082898 0.228643049
## 1093 1094 1095 1096 1097 1098
## 0.155812916 0.034254307 0.255343266 0.106387134 0.015185339 0.298471039
## 1099 1100 1101 1102 1103 1104
## 0.034912244 0.069812487 0.214915014 0.062554819 0.211128336 0.100244086
## 1105 1106 1107 1108 1109 1110
## 0.224586233 0.561736809 0.099887701 0.170255196 0.190440310 0.255781705
## 1111 1112 1113 1114 1115 1116
## 0.191098065 0.006504324 0.054229391 0.243286900 0.215960627 0.423517544
## 1117 1118 1119 1120 1121 1122
## 0.007209921 0.110344404 0.143493468 0.053374864 0.378928180 0.261147926
## 1123 1124 1125 1126 1127 1128
## 0.202662562 0.264852933 0.055110959 0.061975301 0.034219028 0.240280962
## 1129 1130 1131 1132 1133 1134
## 0.208103910 0.035918632 0.181590691 0.134156591 0.153258622 0.156818344
## 1135 1136 1137 1138 1139 1140
## 0.067959474 0.094488860 0.144174258 0.272280379 0.014307843 0.062554218
## 1141 1142 1143 1144 1145 1146
## 0.004334253 0.119583424 0.077008489 0.441256582 0.395548698 0.151302082
## 1147 1148 1149 1150 1151 1152
## 0.028497230 0.136539577 0.070076435 0.131886534 0.088834843 0.197978148
## 1153 1154 1155 1156 1157 1158
## 0.137765059 0.355515095 0.020938422 0.030096646 0.067233820 0.052291820
## 1159 1160 1161 1162 1163 1164
## 0.125599355 0.378017350 0.013256688 0.050074278 0.159398159 0.167127678
## 1165 1166 1167 1168 1169 1170
## 0.159024258 0.128684972 0.005672058 0.239967063 0.362116184 0.178913760
## 1171 1172 1173 1174 1175 1176
## 0.152045307 0.716301391 0.403011551 0.099116496 0.050816805 0.066830443
## 1177 1178 1179 1180 1181 1182
## 0.047485369 0.023644789 0.301219125 0.033329378 0.345351722 0.013174554
## 1183 1184 1185 1186 1187 1188
## 0.038256123 0.084208971 0.012060818 0.013554401 0.198365618 0.061447439
## 1189 1190 1191 1192 1193 1194
## 0.197187746 0.031335356 0.037894059 0.116489201 0.124617865 0.112033957
## 1195 1196 1197 1198 1199 1200
## 0.026575655 0.033322366 0.265374406 0.494323233 0.062511561 0.380315687
## 1201 1202 1203 1204 1205 1206
## 0.034342159 0.184811189 0.134440676 0.034368763 0.068679602 0.164760382
## 1207 1208 1209 1210 1211 1212
## 0.118326428 0.233333611 0.045123945 0.008049620 0.107146888 0.024394843
## 1213 1214 1215 1216 1217 1218
## 0.073930544 0.094388266 0.016537350 0.157623287 0.022959983 0.085633632
## 1219 1220 1221 1222 1223 1224
## 0.148059066 0.166448552 0.150667967 0.022905343 0.427704219 0.113424934
## 1225 1226 1227 1228 1229 1230
## 0.153481655 0.069683639 0.347806162 0.100435729 0.183361161 0.098975527
## 1231 1232 1233 1234 1235 1236
## 0.266965579 0.140843516 0.089368286 0.101880731 0.333875225 0.027010800
## 1237 1238 1239 1240 1241 1242
## 0.228250979 0.458997633 0.389441664 0.331901093 0.021049332 0.287061832
## 1243 1244 1245 1246 1247 1248
## 0.038298251 0.050868489 0.254534246 0.158846923 0.275416369 0.264367761
## 1249 1250 1251 1252 1253 1254
## 0.148627626 0.441692655 0.295599966 0.206247584 0.028860594 0.460946268
## 1255 1256 1257 1258 1259 1260
## 0.211765981 0.625581098 0.088001370 0.329080538 0.188730878 0.107197929
## 1261 1262 1263 1264 1265 1266
## 0.294337954 0.061324031 0.301287555 0.141955193 0.020352030 0.162080004
## 1267 1268 1269 1270 1271 1272
## 0.076350709 0.074916334 0.044568826 0.070943630 0.169043799 0.500394491
## 1273 1274 1275 1276 1277 1278
## 0.055872167 0.171877614 0.297331848 0.067750885 0.164962276 0.006312241
## 1279 1280 1281 1282 1283 1284
## 0.113583821 0.040631627 0.065699592 0.197665567 0.164255559 0.071410065
## 1285 1286 1287 1288 1289 1290
## 0.094748737 0.380179057 0.143617039 0.186608071 0.024606822 0.321786348
## 1291 1292 1293 1294 1295 1296
## 0.153886980 0.362983619 0.078629281 0.437190817 0.295990876 0.041540478
## 1297 1298 1299 1300 1301 1302
## 0.377039937 0.125026702 0.059605033 0.023784194 0.155455765 0.013701646
## 1303 1304 1305 1306 1307 1308
## 0.138846063 0.023200309 0.094987878 0.022930531 0.325214757 0.102578634
## 1309 1310 1311 1312 1313 1314
## 0.111286002 0.174086714 0.030856532 0.633893466 0.314234174 0.638948373
## 1315 1316 1317 1318 1319 1320
## 0.094293903 0.050848994 0.075680510 0.152123358 0.077641045 0.476031456
## 1321 1322 1323 1324 1325 1326
## 0.163013040 0.193321637 0.017353015 0.043259990 0.177965423 0.174787181
## 1327 1328 1329 1330 1331 1332
## 0.355586222 0.106638705 0.207525590 0.085467721 0.032435203 0.008654509
## 1333 1334 1335 1336 1337 1338
## 0.273567229 0.080395200 0.173096466 0.078684483 0.112279990 0.138633437
## 1339 1340 1341 1342 1343 1344
## 0.314863460 0.241080959 0.161650982 0.091136452 0.040144807 0.347248698
## 1345 1346 1347 1348 1349 1350
## 0.112299863 0.067096819 0.055914211 0.284727745 0.027833231 0.136767640
## 1351 1352 1353 1354 1355 1356
## 0.365590534 0.006229578 0.075101590 0.239471158 0.193717667 0.395123032
## 1357 1358 1359 1360 1361 1362
## 0.177956309 0.074016405 0.047855837 0.058812018 0.272354264 0.052236693
## 1363 1364 1365 1366 1367 1368
## 0.104231445 0.373494420 0.050479698 0.727608786 0.353820874 0.202187670
## 1369 1370 1371 1372 1373 1374
## 0.041513268 0.321081728 0.184758762 0.130181038 0.147221286 0.034133439
## 1375 1376 1377 1378 1379 1380
## 0.023731613 0.387245066 0.049746036 0.006813747 0.095096308 0.578783494
## 1381 1382 1383 1384 1385 1386
## 0.368687923 0.297129212 0.103442468 0.148379276 0.247122229 0.065200928
## 1387 1388 1389 1390 1391 1392
## 0.261776723 0.228961901 0.042685897 0.079328846 0.216708044 0.655550649
## 1393 1394 1395 1396 1397 1398
## 0.049899014 0.257432532 0.113645977 0.282949040 0.547526707 0.152813481
## 1399 1400 1401 1402 1403 1404
## 0.040043258 0.084143505 0.044678236 0.042875891 0.038041032 0.174757478
## 1405 1406 1407 1408 1409 1410
## 0.131325853 0.059862372 0.183266170 0.242272752 0.213103501 0.106116239
## 1411 1412 1413 1414 1415 1416
## 0.117272537 0.319979834 0.062391866 0.134124323 0.182035778 0.081817988
## 1417 1418 1419 1420 1421 1422
## 0.048995015 0.223861808 0.111510978 0.155629263 0.038581872 0.029373473
## 1423 1424 1425 1426 1427 1428
## 0.132124475 0.226531207 0.122261182 0.043941092 0.273049156 0.202117945
## 1429 1430 1431 1432 1433 1434
## 0.100702825 0.407607954 0.025873299 0.037643172 0.012580617 0.248870800
## 1435 1436 1437 1438 1439 1440
## 0.166561504 0.119085147 0.431724031 0.027450920 0.467087457 0.066346572
## 1441 1442 1443 1444 1445 1446
## 0.070999839 0.017353107 0.216544031 0.034447950 0.292718261 0.054007998
## 1447 1448 1449 1450 1451 1452
## 0.205727324 0.082048360 0.038900760 0.359649635 0.098794440 0.116046834
## 1453 1454 1455 1456 1457 1458
## 0.064523350 0.159210644 0.374344992 0.131853974 0.088732782 0.052976046
## 1459 1460 1461 1462 1463 1464
## 0.036010235 0.117660442 0.613047626 0.153189272 0.070188518 0.119545508
## 1465 1466 1467 1468 1469 1470
## 0.259058957 0.088686940 0.054833042 0.070940584 0.056512232 0.106520714
attrition_data$Attrition
## [1] Yes No Yes No No No No No No No No No No No Yes No No No
## [19] No No No Yes No No Yes No Yes No No No No No No Yes Yes No
## [37] Yes No No No No No Yes No No Yes No No No No Yes Yes No No
## [55] No No No No No No No No No No No No No No No Yes No No
## [73] No No No No No No No No No No No No No No No No No Yes
## [91] No No No No No No No No No No Yes No Yes No No No No Yes
## [109] No No No Yes No No No No No No No No No No Yes No Yes No
## [127] Yes Yes No No No No Yes No No No Yes No No No Yes No No No
## [145] No No No No No No No No No No No No No No No No No No
## [163] No No No No No No No No No Yes No No No No No Yes No No
## [181] No No Yes No No No No No No No No No Yes No No No No No
## [199] No No No No No No Yes Yes No No No No Yes No No No Yes No
## [217] Yes Yes No No No No No No No No No No No Yes No No No No
## [235] Yes No Yes No No Yes No No No No No No No No No No Yes No
## [253] No No No No No No No Yes No No No No Yes No No No No No
## [271] No Yes No No No No No No No No No No No No No No Yes No
## [289] Yes No No No No Yes No No Yes No No No No No No No No No
## [307] No No No No No No No No No No No Yes No No No No No Yes
## [325] No No No Yes No No No No No No No No Yes No No No No No
## [343] No No No No No No No No No No No No No No No Yes No No
## [361] No No No Yes No No Yes No Yes No Yes No No No No No No No
## [379] Yes No No No Yes No No Yes No No No No No No No No No No
## [397] No No No No No No No No No Yes No No No No No No No No
## [415] Yes Yes No No No No No Yes Yes No No No No No No No No No
## [433] No No No Yes Yes No No Yes Yes No No Yes No No No No No No
## [451] No No No Yes No No No Yes No No No No No Yes No No No No
## [469] No Yes No No No No No No No No No Yes Yes No Yes No No No
## [487] No No No No No No No No No Yes No No No No No No No No
## [505] Yes No No No No No No No No Yes Yes No No No No No No No
## [523] No No No Yes No No Yes No No No No No No No No No No No
## [541] Yes No No No No No No Yes No No No No No No No No No No
## [559] No No No No Yes No No No Yes No Yes No No No No Yes No No
## [577] No No No No No No No No No Yes No No No Yes No Yes No No
## [595] No Yes No No Yes No No No No No No No No Yes Yes No No No
## [613] No No Yes No No No No No No No No No No No No No No No
## [631] No No No No No No Yes No No No No No No No No Yes No No
## [649] No No No No No No No No Yes No No No Yes No Yes Yes No No
## [667] Yes Yes No Yes No No No No No No No No No No No No No Yes
## [685] No No No No Yes Yes No No No Yes No Yes No No No No Yes No
## [703] No No No No Yes No No Yes No Yes No No No No No No No No
## [721] Yes No No No No Yes No No No No No Yes Yes No No No No No
## [739] No No No No No No Yes No No No Yes Yes No No Yes No No No
## [757] No No No No No Yes Yes No No No No No No No No No No No
## [775] No No Yes Yes No Yes Yes No No No No No No No No Yes No Yes
## [793] Yes No No No Yes Yes Yes No Yes Yes No No No No No No No No
## [811] No No No Yes No No No No No No No No No No No No No No
## [829] Yes Yes No Yes No No No No Yes No Yes No No No Yes No No No
## [847] No No No Yes No No No No No No No Yes No No Yes No No No
## [865] Yes No No No No No No Yes No No No No No No No No No No
## [883] No No No No No No No No No No Yes No No No No No No No
## [901] No No No No No No No No No No No Yes No Yes No Yes No No
## [919] No No No No No No No No No No Yes No No No Yes No No No
## [937] No No No Yes Yes No No No No No Yes Yes No No No No Yes Yes
## [955] No No No No No No No No No No No No Yes No No No No No
## [973] No No No Yes No No No No Yes Yes No No No Yes No No No No
## [991] No No No No No No No Yes No No No No No No No No Yes Yes
## [1009] No No No No Yes No No No Yes No No No No Yes No No No No
## [1027] No No No No No Yes Yes Yes No No Yes No No Yes No No No No
## [1045] No No No No No No No No No No No No Yes Yes Yes No Yes No
## [1063] No No No No No No Yes No No No No No No No No Yes No No
## [1081] No No No Yes No Yes No No No No No No No No No No No No
## [1099] No No No No No No No No Yes No No No Yes Yes Yes No No No
## [1117] No No No No No No No No No No No No No No No No No No
## [1135] No No Yes No No No No No No No No No No No No No No No
## [1153] No Yes No No No No No No No No Yes No No No No Yes No No
## [1171] No Yes No No No No No No No No No No No No No No Yes No
## [1189] No No No No No No No No No No No No No Yes No No Yes Yes
## [1207] No No No No No No No Yes No No No No No No No No Yes Yes
## [1225] No No No No No No No No No No No No Yes Yes No No No No
## [1243] No No No No Yes No No Yes No No No No No Yes No Yes No No
## [1261] No No Yes No No No No No No No No Yes No Yes No No No No
## [1279] No Yes No Yes No No No No No No No No Yes Yes No No No No
## [1297] No Yes Yes No No No No No No No No No No No No No Yes Yes
## [1315] No No No No No No No No No No No No Yes No No No No No
## [1333] Yes Yes No No No No Yes Yes No No No No No No No No No No
## [1351] No No No Yes Yes No No No No No No No No No No Yes No No
## [1369] No Yes No No No No No Yes No No No Yes No No No No No No
## [1387] No No No No Yes No No No No Yes Yes No No No No No No No
## [1405] No No No No No No No No No No No No No No No No No No
## [1423] No No No No No No No No No No No No No No No No Yes No
## [1441] No No Yes No Yes No No No No No No No Yes No No No No No
## [1459] No No No Yes No No No No No No No No
## Levels: No Yes
pdataN <- as.factor(ifelse(test=as.numeric(pdata>0.5) == 0, yes="No", no="Yes"))
#Each value in the pdata object represents the predicted probability of Attrition being "Yes" for the corresponding observation in your dataset.
# From pROC
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
par(pty = "s")
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage")
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage")
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 0.7691
## If we want to find out the optimal threshold we can store the
## data used to make the ROC graph in a variable...
roc.info <- roc(attrition_data$Attrition, logistic$fitted.values, legacy.axes=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
str(roc.info)
## List of 15
## $ percent : logi FALSE
## $ sensitivities : num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
## $ specificities : num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
## $ thresholds : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
## $ direction : chr "<"
## $ cases : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
## ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
## $ controls : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
## ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
## $ fun.sesp :function (thresholds, controls, cases, direction)
## $ auc : 'auc' num 0.769
## ..- attr(*, "partial.auc")= logi FALSE
## ..- attr(*, "percent")= logi FALSE
## ..- attr(*, "roc")=List of 15
## .. ..$ percent : logi FALSE
## .. ..$ sensitivities : num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
## .. ..$ specificities : num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
## .. ..$ thresholds : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
## .. ..$ direction : chr "<"
## .. ..$ cases : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
## .. .. ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
## .. ..$ controls : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
## .. .. ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
## .. ..$ fun.sesp :function (thresholds, controls, cases, direction)
## .. ..$ auc : 'auc' num 0.769
## .. .. ..- attr(*, "partial.auc")= logi FALSE
## .. .. ..- attr(*, "percent")= logi FALSE
## .. .. ..- attr(*, "roc")=List of 8
## .. .. .. ..$ percent : logi FALSE
## .. .. .. ..$ sensitivities: num [1:1471] 1 1 1 1 1 1 1 1 1 1 ...
## .. .. .. ..$ specificities: num [1:1471] 0 0.000811 0.001622 0.002433 0.003244 ...
## .. .. .. ..$ thresholds : num [1:1471] -Inf 0.00282 0.00362 0.00435 0.00448 ...
## .. .. .. ..$ direction : chr "<"
## .. .. .. ..$ cases : Named num [1:237] 0.408 0.229 0.429 0.474 0.265 ...
## .. .. .. .. ..- attr(*, "names")= chr [1:237] "1" "3" "15" "22" ...
## .. .. .. ..$ controls : Named num [1:1233] 0.0326 0.0599 0.3011 0.1084 0.0824 ...
## .. .. .. .. ..- attr(*, "names")= chr [1:1233] "2" "4" "5" "6" ...
## .. .. .. ..$ fun.sesp :function (thresholds, controls, cases, direction)
## .. .. .. ..- attr(*, "class")= chr "roc"
## .. ..$ call : language roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, legacy.axes = TRUE)
## .. ..$ original.predictor: Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
## .. .. ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
## .. ..$ original.response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## .. ..$ predictor : Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
## .. .. ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
## .. ..$ response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## .. ..$ levels : chr [1:2] "No" "Yes"
## .. ..- attr(*, "class")= chr "roc"
## $ call : language roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, legacy.axes = TRUE)
## $ original.predictor: Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
## ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
## $ original.response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## $ predictor : Named num [1:1470] 0.4085 0.0326 0.2287 0.0599 0.3011 ...
## ..- attr(*, "names")= chr [1:1470] "1" "2" "3" "4" ...
## $ response : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## $ levels : chr [1:2] "No" "Yes"
## - attr(*, "class")= chr "roc"
## tpp = true positive percentage
## fpp = false positive precentage
roc.df <- data.frame(tpp=roc.info$sensitivities*100, fpp=(1 - roc.info$specificities)*100,thresholds=roc.info$thresholds)
roc.df
## tpp fpp thresholds
## 1 100.0000000 100.000000 -Inf
## 2 100.0000000 99.918897 0.002818221
## 3 100.0000000 99.837794 0.003621546
## 4 100.0000000 99.756691 0.004351793
## 5 100.0000000 99.675588 0.004477370
## 6 100.0000000 99.594485 0.004686418
## 7 100.0000000 99.513382 0.004926309
## 8 100.0000000 99.432279 0.005121393
## 9 100.0000000 99.351176 0.005219730
## 10 100.0000000 99.270073 0.005285951
## 11 100.0000000 99.188970 0.005491048
## 12 100.0000000 99.107867 0.005733764
## 13 100.0000000 99.026764 0.005919943
## 14 100.0000000 98.945661 0.006119448
## 15 100.0000000 98.864558 0.006212029
## 16 100.0000000 98.783455 0.006270910
## 17 100.0000000 98.702352 0.006321684
## 18 100.0000000 98.621249 0.006412049
## 19 100.0000000 98.540146 0.006498648
## 20 99.5780591 98.540146 0.006548473
## 21 99.5780591 98.459043 0.006610525
## 22 99.5780591 98.377940 0.006659565
## 23 99.5780591 98.296837 0.006752225
## 24 99.5780591 98.215734 0.006819119
## 25 99.5780591 98.134631 0.006856867
## 26 99.5780591 98.053528 0.007049582
## 27 99.5780591 97.972425 0.007219340
## 28 99.5780591 97.891322 0.007501932
## 29 99.5780591 97.810219 0.007826828
## 30 99.5780591 97.729116 0.007964085
## 31 99.5780591 97.648013 0.008170363
## 32 99.1561181 97.648013 0.008309149
## 33 99.1561181 97.566910 0.008387801
## 34 99.1561181 97.485807 0.008454758
## 35 99.1561181 97.404704 0.008557807
## 36 99.1561181 97.323601 0.008784000
## 37 99.1561181 97.242498 0.009030731
## 38 99.1561181 97.161395 0.009249295
## 39 99.1561181 97.080292 0.009384072
## 40 99.1561181 96.999189 0.009510375
## 41 99.1561181 96.918086 0.009655213
## 42 99.1561181 96.836983 0.009768345
## 43 99.1561181 96.755880 0.009857626
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## 868 74.6835443 34.549878 0.147391415
## 869 74.6835443 34.468775 0.147731906
## 870 74.6835443 34.387672 0.148087966
## 871 74.6835443 34.306569 0.148248071
## 872 74.6835443 34.225466 0.148408396
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## 874 74.6835443 34.063260 0.148909478
## 875 74.6835443 33.982157 0.149299645
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## 879 74.2616034 33.738848 0.150791762
## 880 74.2616034 33.657745 0.151023181
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## 882 74.2616034 33.495539 0.151377903
## 883 73.8396624 33.495539 0.151605814
## 884 73.8396624 33.414436 0.151788734
## 885 73.8396624 33.333333 0.151932436
## 886 73.8396624 33.252230 0.152084332
## 887 73.8396624 33.171127 0.152446302
## 888 73.8396624 33.090024 0.152791363
## 889 73.8396624 33.008921 0.152999186
## 890 73.8396624 32.927818 0.153187081
## 891 73.4177215 32.927818 0.153223947
## 892 73.4177215 32.846715 0.153285240
## 893 73.4177215 32.765612 0.153396756
## 894 73.4177215 32.684509 0.153486519
## 895 73.4177215 32.603406 0.153675337
## 896 73.4177215 32.522303 0.153873135
## 897 72.9957806 32.522303 0.153896153
## 898 72.9957806 32.441200 0.153917047
## 899 72.9957806 32.360097 0.154081359
## 900 72.9957806 32.278994 0.154328751
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## 903 72.9957806 32.035685 0.155058534
## 904 72.9957806 31.954582 0.155262815
## 905 72.9957806 31.873479 0.155542514
## 906 72.9957806 31.792376 0.155721089
## 907 72.9957806 31.711273 0.155862007
## 908 72.9957806 31.630170 0.156096030
## 909 72.9957806 31.549067 0.156293855
## 910 72.9957806 31.467964 0.156562546
## 911 72.9957806 31.386861 0.156825332
## 912 72.9957806 31.305758 0.156966936
## 913 72.9957806 31.224655 0.157282065
## 914 72.9957806 31.143552 0.157542933
## 915 72.9957806 31.062449 0.157892467
## 916 72.9957806 30.981346 0.158287096
## 917 72.9957806 30.900243 0.158457140
## 918 72.9957806 30.819140 0.158561975
## 919 72.5738397 30.819140 0.158734568
## 920 72.5738397 30.738037 0.158935590
## 921 72.5738397 30.656934 0.159101371
## 922 72.5738397 30.575831 0.159194565
## 923 72.5738397 30.494728 0.159304402
## 924 72.1518987 30.494728 0.160105078
## 925 72.1518987 30.413625 0.161074603
## 926 72.1518987 30.332522 0.161494095
## 927 72.1518987 30.251419 0.161810460
## 928 72.1518987 30.170316 0.162024971
## 929 72.1518987 30.089213 0.162137776
## 930 72.1518987 30.008110 0.162366102
## 931 72.1518987 29.927007 0.162586685
## 932 72.1518987 29.845904 0.162824877
## 933 72.1518987 29.764801 0.163327320
## 934 71.7299578 29.764801 0.163643646
## 935 71.7299578 29.683698 0.163810617
## 936 71.7299578 29.602595 0.164115550
## 937 71.7299578 29.521492 0.164507971
## 938 71.3080169 29.521492 0.164803675
## 939 71.3080169 29.440389 0.164904622
## 940 71.3080169 29.359286 0.165038422
## 941 71.3080169 29.278183 0.165117658
## 942 71.3080169 29.197080 0.165240952
## 943 71.3080169 29.115977 0.165385924
## 944 71.3080169 29.034874 0.165568786
## 945 71.3080169 28.953771 0.165788824
## 946 71.3080169 28.872668 0.166048191
## 947 71.3080169 28.791565 0.166347084
## 948 71.3080169 28.710462 0.166505028
## 949 71.3080169 28.629359 0.166839969
## 950 71.3080169 28.548256 0.167123056
## 951 71.3080169 28.467153 0.167191013
## 952 71.3080169 28.386050 0.167483992
## 953 71.3080169 28.304947 0.168215332
## 954 71.3080169 28.223844 0.168855815
## 955 71.3080169 28.142741 0.169019200
## 956 71.3080169 28.061638 0.169081806
## 957 71.3080169 27.980535 0.169210360
## 958 70.8860759 27.980535 0.169447499
## 959 70.8860759 27.899432 0.169651093
## 960 70.8860759 27.818329 0.169892730
## 961 70.8860759 27.737226 0.170166281
## 962 70.8860759 27.656123 0.170387815
## 963 70.8860759 27.575020 0.170582178
## 964 70.4641350 27.575020 0.170664006
## 965 70.4641350 27.493917 0.170870096
## 966 70.4641350 27.412814 0.171135735
## 967 70.0421941 27.412814 0.171546490
## 968 69.6202532 27.412814 0.171945608
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## 970 69.1983122 27.331711 0.172306921
## 971 69.1983122 27.250608 0.172756719
## 972 68.7763713 27.250608 0.173031447
## 973 68.7763713 27.169505 0.173089068
## 974 68.7763713 27.088402 0.173201932
## 975 68.7763713 27.007299 0.173346469
## 976 68.7763713 26.926196 0.173736127
## 977 68.7763713 26.845093 0.174217124
## 978 68.7763713 26.763990 0.174552506
## 979 68.7763713 26.682887 0.174772329
## 980 68.7763713 26.601784 0.174790531
## 981 68.7763713 26.520681 0.174874399
## 982 68.3544304 26.520681 0.175021000
## 983 68.3544304 26.439578 0.175129638
## 984 68.3544304 26.358475 0.175267971
## 985 68.3544304 26.277372 0.175426458
## 986 67.9324895 26.277372 0.175562464
## 987 67.9324895 26.196269 0.175970298
## 988 67.9324895 26.115166 0.176454247
## 989 67.9324895 26.034063 0.176903586
## 990 67.9324895 25.952960 0.177579910
## 991 67.9324895 25.871857 0.177960866
## 992 67.9324895 25.790754 0.178439591
## 993 67.9324895 25.709651 0.178920074
## 994 67.9324895 25.628548 0.179267121
## 995 67.9324895 25.547445 0.180411793
## 996 67.9324895 25.466342 0.181325425
## 997 67.9324895 25.385239 0.181445402
## 998 67.9324895 25.304136 0.181474829
## 999 67.9324895 25.223033 0.181542332
## 1000 67.9324895 25.141930 0.181813234
## 1001 67.9324895 25.060827 0.182650974
## 1002 67.9324895 24.979724 0.183313666
## 1003 67.9324895 24.898621 0.183420768
## 1004 67.5105485 24.898621 0.183834490
## 1005 67.5105485 24.817518 0.184473683
## 1006 67.5105485 24.736415 0.184784975
## 1007 67.0886076 24.736415 0.185145452
## 1008 67.0886076 24.655312 0.185525589
## 1009 67.0886076 24.574209 0.185890980
## 1010 67.0886076 24.493106 0.186359155
## 1011 66.6666667 24.493106 0.186557942
## 1012 66.6666667 24.412003 0.186611517
## 1013 66.6666667 24.330900 0.186916228
## 1014 66.6666667 24.249797 0.187295941
## 1015 66.6666667 24.168694 0.187529915
## 1016 66.6666667 24.087591 0.187973879
## 1017 66.6666667 24.006488 0.188475549
## 1018 66.6666667 23.925385 0.188709830
## 1019 66.6666667 23.844282 0.189044912
## 1020 66.6666667 23.763179 0.189472138
## 1021 66.6666667 23.682076 0.190012821
## 1022 66.6666667 23.600973 0.190455153
## 1023 66.6666667 23.519870 0.190614877
## 1024 66.6666667 23.438767 0.190928912
## 1025 66.2447257 23.438767 0.192046165
## 1026 66.2447257 23.357664 0.193157951
## 1027 66.2447257 23.276561 0.193519652
## 1028 65.8227848 23.276561 0.193788936
## 1029 65.8227848 23.195458 0.193876491
## 1030 65.4008439 23.195458 0.194173391
## 1031 65.4008439 23.114355 0.195224056
## 1032 64.9789030 23.114355 0.196095347
## 1033 64.9789030 23.033252 0.196259655
## 1034 64.9789030 22.952149 0.196520772
## 1035 64.9789030 22.871046 0.196953283
## 1036 64.9789030 22.789943 0.197331082
## 1037 64.5569620 22.789943 0.197507851
## 1038 64.5569620 22.708840 0.197556336
## 1039 64.5569620 22.627737 0.197618478
## 1040 64.1350211 22.627737 0.197821858
## 1041 64.1350211 22.546634 0.198054475
## 1042 64.1350211 22.465531 0.198248210
## 1043 63.7130802 22.465531 0.198727781
## 1044 63.7130802 22.384428 0.199172775
## 1045 63.2911392 22.384428 0.199275636
## 1046 63.2911392 22.303325 0.199324683
## 1047 63.2911392 22.222222 0.199429207
## 1048 63.2911392 22.141119 0.199547414
## 1049 62.8691983 22.141119 0.199863124
## 1050 62.8691983 22.060016 0.200229266
## 1051 62.8691983 21.978913 0.200892577
## 1052 62.8691983 21.897810 0.201625243
## 1053 62.8691983 21.816707 0.201952837
## 1054 62.8691983 21.735604 0.202152808
## 1055 62.8691983 21.654501 0.202425116
## 1056 62.8691983 21.573398 0.202935676
## 1057 62.8691983 21.492295 0.203394852
## 1058 62.8691983 21.411192 0.203812822
## 1059 62.8691983 21.330089 0.204075003
## 1060 62.8691983 21.248986 0.204636777
## 1061 62.8691983 21.167883 0.205447801
## 1062 62.8691983 21.086780 0.205894500
## 1063 62.8691983 21.005677 0.206114212
## 1064 62.8691983 20.924574 0.206207166
## 1065 62.8691983 20.843471 0.206270667
## 1066 62.4472574 20.843471 0.206592781
## 1067 62.4472574 20.762368 0.207158820
## 1068 62.4472574 20.681265 0.207475709
## 1069 62.4472574 20.600162 0.207647152
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## 1071 62.4472574 20.437956 0.208133422
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## 1073 62.0253165 20.356853 0.208721526
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## 1077 62.0253165 20.032441 0.209940208
## 1078 61.6033755 20.032441 0.210563842
## 1079 61.6033755 19.951338 0.211285304
## 1080 61.6033755 19.870235 0.211559434
## 1081 61.6033755 19.789132 0.211721288
## 1082 61.6033755 19.708029 0.211852438
## 1083 61.6033755 19.626926 0.211955374
## 1084 61.1814346 19.626926 0.212537677
## 1085 61.1814346 19.545823 0.213195144
## 1086 61.1814346 19.464720 0.213392072
## 1087 61.1814346 19.383617 0.213571054
## 1088 61.1814346 19.302514 0.213733613
## 1089 61.1814346 19.221411 0.214368744
## 1090 61.1814346 19.140308 0.215296755
## 1091 60.7594937 19.140308 0.215744759
## 1092 60.7594937 19.059205 0.215817677
## 1093 60.3375527 19.059205 0.215892480
## 1094 60.3375527 18.978102 0.216027306
## 1095 60.3375527 18.896999 0.216319008
## 1096 59.9156118 18.896999 0.216626037
## 1097 59.4936709 18.896999 0.216752417
## 1098 59.4936709 18.815896 0.217262555
## 1099 59.0717300 18.815896 0.217760231
## 1100 59.0717300 18.734793 0.217947899
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## 1103 59.0717300 18.491484 0.221704072
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## 1107 59.0717300 18.167072 0.222757345
## 1108 59.0717300 18.085969 0.222860425
## 1109 58.6497890 18.085969 0.223195465
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## 1111 57.8059072 18.085969 0.223734905
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## 1113 57.8059072 17.923763 0.224733345
## 1114 57.8059072 17.842660 0.224889708
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## 1116 57.8059072 17.680454 0.226529302
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## 1148 54.0084388 15.815085 0.240124012
## 1149 54.0084388 15.733982 0.240329638
## 1150 54.0084388 15.652879 0.240467576
## 1151 54.0084388 15.571776 0.240596401
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## 1158 53.1645570 15.166261 0.242667430
## 1159 53.1645570 15.085158 0.243089518
## 1160 53.1645570 15.004055 0.243503500
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## 1165 53.1645570 14.598540 0.245304206
## 1166 53.1645570 14.517437 0.245692400
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## 1168 52.7426160 14.436334 0.246506710
## 1169 52.7426160 14.355231 0.247683496
## 1170 52.7426160 14.274128 0.248557782
## 1171 52.7426160 14.193025 0.250194992
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## 1173 52.7426160 14.030819 0.253017053
## 1174 52.7426160 13.949716 0.253840377
## 1175 52.7426160 13.868613 0.254486175
## 1176 52.7426160 13.787510 0.254902912
## 1177 52.7426160 13.706407 0.255307422
## 1178 52.7426160 13.625304 0.255562486
## 1179 52.7426160 13.544201 0.255790030
## 1180 52.7426160 13.463098 0.256615444
## 1181 52.7426160 13.381995 0.258077787
## 1182 52.3206751 13.381995 0.258891000
## 1183 52.3206751 13.300892 0.259133891
## 1184 52.3206751 13.219789 0.259225664
## 1185 51.8987342 13.219789 0.259582772
## 1186 51.8987342 13.138686 0.260535483
## 1187 51.8987342 13.057583 0.261462324
## 1188 51.8987342 12.976480 0.262303395
## 1189 51.8987342 12.895377 0.262862423
## 1190 51.8987342 12.814274 0.263473924
## 1191 51.8987342 12.733171 0.264210416
## 1192 51.8987342 12.652068 0.264460467
## 1193 51.4767932 12.652068 0.264703053
## 1194 51.4767932 12.570965 0.265113669
## 1195 51.4767932 12.489862 0.265909926
## 1196 51.4767932 12.408759 0.266466832
## 1197 51.0548523 12.408759 0.266726899
## 1198 51.0548523 12.327656 0.267246044
## 1199 51.0548523 12.246553 0.267888112
## 1200 51.0548523 12.165450 0.268427064
## 1201 51.0548523 12.084347 0.268819123
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## 1203 50.6329114 12.003244 0.269448648
## 1204 50.6329114 11.922141 0.269809381
## 1205 50.6329114 11.841038 0.270036536
## 1206 50.2109705 11.841038 0.270909233
## 1207 50.2109705 11.759935 0.271987893
## 1208 50.2109705 11.678832 0.272259264
## 1209 50.2109705 11.597729 0.272317321
## 1210 50.2109705 11.516626 0.272385107
## 1211 49.7890295 11.516626 0.272732552
## 1212 49.7890295 11.435523 0.273063548
## 1213 49.7890295 11.354420 0.273221201
## 1214 49.3670886 11.354420 0.273465845
## 1215 48.9451477 11.354420 0.273910478
## 1216 48.9451477 11.273317 0.274262406
## 1217 48.9451477 11.192214 0.274843727
## 1218 48.5232068 11.192214 0.276091415
## 1219 48.1012658 11.192214 0.276921178
## 1220 47.6793249 11.192214 0.277651863
## 1221 47.2573840 11.192214 0.278272072
## 1222 47.2573840 11.111111 0.279245086
## 1223 46.8354430 11.111111 0.281418611
## 1224 46.8354430 11.030008 0.282806201
## 1225 46.4135021 11.030008 0.283722655
## 1226 46.4135021 10.948905 0.284612008
## 1227 46.4135021 10.867802 0.284963911
## 1228 46.4135021 10.786699 0.285496732
## 1229 46.4135021 10.705596 0.285834122
## 1230 45.9915612 10.705596 0.285914327
## 1231 45.5696203 10.705596 0.286132077
## 1232 45.5696203 10.624493 0.286686094
## 1233 45.5696203 10.543390 0.288936973
## 1234 45.1476793 10.543390 0.291765188
## 1235 44.7257384 10.543390 0.292772107
## 1236 44.7257384 10.462287 0.293042544
## 1237 44.7257384 10.381184 0.293358538
## 1238 44.7257384 10.300081 0.293521223
## 1239 44.3037975 10.300081 0.293596815
## 1240 44.3037975 10.218978 0.293773123
## 1241 44.3037975 10.137875 0.294137537
## 1242 44.3037975 10.056772 0.294624286
## 1243 43.8818565 10.056772 0.295114296
## 1244 43.8818565 9.975669 0.295458969
## 1245 43.8818565 9.894566 0.295795421
## 1246 43.8818565 9.813463 0.296090410
## 1247 43.8818565 9.732360 0.296248797
## 1248 43.4599156 9.732360 0.296603325
## 1249 43.4599156 9.651257 0.297014106
## 1250 43.4599156 9.570154 0.297230530
## 1251 43.4599156 9.489051 0.297901443
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## 1254 42.6160338 9.407948 0.299342740
## 1255 42.6160338 9.326845 0.300149194
## 1256 42.1940928 9.326845 0.300754811
## 1257 42.1940928 9.245742 0.300948748
## 1258 42.1940928 9.164639 0.301178532
## 1259 42.1940928 9.083536 0.301253340
## 1260 41.7721519 9.083536 0.302118869
## 1261 41.3502110 9.083536 0.303082913
## 1262 40.9282700 9.083536 0.304234491
## 1263 40.5063291 9.083536 0.306239923
## 1264 40.5063291 9.002433 0.307280272
## 1265 40.5063291 8.921330 0.307435422
## 1266 40.5063291 8.840227 0.307735107
## 1267 40.5063291 8.759124 0.308292783
## 1268 40.5063291 8.678021 0.310680912
## 1269 40.5063291 8.596918 0.313432256
## 1270 40.0843882 8.596918 0.314194511
## 1271 39.6624473 8.596918 0.314421260
## 1272 39.2405063 8.596918 0.314735903
## 1273 38.8185654 8.596918 0.315359608
## 1274 38.8185654 8.515815 0.316328864
## 1275 38.8185654 8.434712 0.318018050
## 1276 38.3966245 8.434712 0.319606981
## 1277 38.3966245 8.353609 0.320530781
## 1278 37.9746835 8.353609 0.321434038
## 1279 37.9746835 8.272506 0.321935967
## 1280 37.5527426 8.272506 0.322108031
## 1281 37.1308017 8.272506 0.322378066
## 1282 37.1308017 8.191403 0.323920206
## 1283 37.1308017 8.110300 0.325440203
## 1284 37.1308017 8.029197 0.325796741
## 1285 36.7088608 8.029197 0.326613563
## 1286 36.7088608 7.948094 0.327647431
## 1287 36.7088608 7.866991 0.328120083
## 1288 36.7088608 7.785888 0.328662567
## 1289 36.2869198 7.785888 0.330063202
## 1290 36.2869198 7.704785 0.331090817
## 1291 35.8649789 7.704785 0.331518430
## 1292 35.8649789 7.623682 0.332420712
## 1293 35.8649789 7.542579 0.333353047
## 1294 35.8649789 7.461476 0.333820494
## 1295 35.8649789 7.380373 0.333903137
## 1296 35.8649789 7.299270 0.334114610
## 1297 35.8649789 7.218167 0.336610624
## 1298 35.8649789 7.137064 0.339422125
## 1299 35.8649789 7.055961 0.340141943
## 1300 35.4430380 7.055961 0.341101209
## 1301 35.4430380 6.974858 0.342982074
## 1302 35.0210970 6.974858 0.344738084
## 1303 35.0210970 6.893755 0.345443053
## 1304 34.5991561 6.893755 0.345925564
## 1305 34.5991561 6.812652 0.346782721
## 1306 34.5991561 6.731549 0.347527430
## 1307 34.5991561 6.650446 0.348442367
## 1308 34.5991561 6.569343 0.349254913
## 1309 34.1772152 6.569343 0.350458354
## 1310 33.7552743 6.569343 0.352156299
## 1311 33.7552743 6.488240 0.353324010
## 1312 33.7552743 6.407137 0.353902847
## 1313 33.7552743 6.326034 0.354749957
## 1314 33.3333333 6.326034 0.355550658
## 1315 32.9113924 6.326034 0.356104085
## 1316 32.9113924 6.244931 0.356854948
## 1317 32.9113924 6.163828 0.357459965
## 1318 32.9113924 6.082725 0.357855172
## 1319 32.9113924 6.001622 0.358446793
## 1320 32.4894515 6.001622 0.359332429
## 1321 32.4894515 5.920519 0.360413573
## 1322 32.4894515 5.839416 0.361601706
## 1323 32.4894515 5.758313 0.362032343
## 1324 32.0675105 5.758313 0.362077485
## 1325 32.0675105 5.677210 0.362348770
## 1326 31.6455696 5.677210 0.362782487
## 1327 31.2236287 5.677210 0.363017855
## 1328 31.2236287 5.596107 0.363583406
## 1329 31.2236287 5.515004 0.364121094
## 1330 30.8016878 5.515004 0.364859001
## 1331 30.8016878 5.433901 0.366273876
## 1332 30.3797468 5.433901 0.367822571
## 1333 30.3797468 5.352798 0.369064001
## 1334 30.3797468 5.271695 0.370845720
## 1335 30.3797468 5.190592 0.372561765
## 1336 29.9578059 5.190592 0.373093176
## 1337 29.5358650 5.190592 0.373404301
## 1338 29.5358650 5.109489 0.373607564
## 1339 29.1139241 5.109489 0.373934016
## 1340 29.1139241 5.028386 0.374246158
## 1341 29.1139241 4.947283 0.374708179
## 1342 29.1139241 4.866180 0.375216775
## 1343 29.1139241 4.785077 0.376201061
## 1344 29.1139241 4.703974 0.377528644
## 1345 29.1139241 4.622871 0.378472765
## 1346 29.1139241 4.541768 0.379553619
## 1347 29.1139241 4.460665 0.380247372
## 1348 29.1139241 4.379562 0.381586046
## 1349 29.1139241 4.298459 0.383465666
## 1350 28.6919831 4.298459 0.384248864
## 1351 28.6919831 4.217356 0.385547313
## 1352 28.6919831 4.136253 0.386958445
## 1353 28.2700422 4.136253 0.387718024
## 1354 28.2700422 4.055150 0.388518891
## 1355 27.8481013 4.055150 0.389144232
## 1356 27.8481013 3.974047 0.390602007
## 1357 27.8481013 3.892944 0.392369866
## 1358 27.8481013 3.811841 0.392988802
## 1359 27.4261603 3.811841 0.393287238
## 1360 27.0042194 3.811841 0.393895314
## 1361 27.0042194 3.730738 0.394315363
## 1362 26.5822785 3.730738 0.394768691
## 1363 26.5822785 3.649635 0.395335865
## 1364 26.5822785 3.568532 0.396036870
## 1365 26.1603376 3.568532 0.398023993
## 1366 26.1603376 3.487429 0.401267247
## 1367 26.1603376 3.406326 0.403726856
## 1368 25.7383966 3.406326 0.406025058
## 1369 25.7383966 3.325223 0.408050274
## 1370 25.3164557 3.325223 0.408727181
## 1371 25.3164557 3.244120 0.409080720
## 1372 24.8945148 3.244120 0.409242814
## 1373 24.8945148 3.163017 0.409570991
## 1374 24.8945148 3.081914 0.411379741
## 1375 24.8945148 3.000811 0.413178621
## 1376 24.4725738 3.000811 0.415445927
## 1377 24.4725738 2.919708 0.417529189
## 1378 24.4725738 2.838605 0.418098871
## 1379 24.0506329 2.838605 0.419105907
## 1380 24.0506329 2.757502 0.420333244
## 1381 24.0506329 2.676399 0.422274824
## 1382 24.0506329 2.595296 0.423538853
## 1383 24.0506329 2.514193 0.425632190
## 1384 23.6286920 2.514193 0.428184576
## 1385 23.2067511 2.514193 0.429192394
## 1386 22.7848101 2.514193 0.430721942
## 1387 22.7848101 2.433090 0.432345263
## 1388 22.7848101 2.351987 0.435078656
## 1389 22.7848101 2.270884 0.437524202
## 1390 22.7848101 2.189781 0.439557084
## 1391 22.7848101 2.108678 0.441474618
## 1392 22.3628692 2.108678 0.441991729
## 1393 21.9409283 2.108678 0.446336686
## 1394 21.9409283 2.027575 0.452320188
## 1395 21.5189873 2.027575 0.456027684
## 1396 21.0970464 2.027575 0.457847834
## 1397 20.6751055 2.027575 0.458447870
## 1398 20.2531646 2.027575 0.459971951
## 1399 20.2531646 1.946472 0.460969723
## 1400 19.8312236 1.946472 0.461397031
## 1401 19.4092827 1.946472 0.462957851
## 1402 19.4092827 1.865369 0.464468715
## 1403 19.4092827 1.784266 0.464988894
## 1404 19.4092827 1.703163 0.466121317
## 1405 18.9873418 1.703163 0.467457348
## 1406 18.5654008 1.703163 0.469570331
## 1407 18.5654008 1.622060 0.472598698
## 1408 18.1434599 1.622060 0.474331514
## 1409 17.7215190 1.622060 0.475405256
## 1410 17.7215190 1.540957 0.476990199
## 1411 17.2995781 1.540957 0.478595683
## 1412 16.8776371 1.540957 0.480587600
## 1413 16.4556962 1.540957 0.484760284
## 1414 16.4556962 1.459854 0.490255077
## 1415 16.0337553 1.459854 0.492975137
## 1416 15.6118143 1.459854 0.493675574
## 1417 15.6118143 1.378751 0.495671765
## 1418 15.6118143 1.297648 0.497380207
## 1419 15.1898734 1.297648 0.499067304
## 1420 14.7679325 1.297648 0.500822412
## 1421 14.3459916 1.297648 0.502239054
## 1422 14.3459916 1.216545 0.503430459
## 1423 14.3459916 1.135442 0.504056510
## 1424 13.9240506 1.135442 0.506928247
## 1425 13.9240506 1.054339 0.512272476
## 1426 13.5021097 1.054339 0.518452857
## 1427 13.5021097 0.973236 0.523398231
## 1428 13.0801688 0.973236 0.525166630
## 1429 13.0801688 0.892133 0.530507392
## 1430 12.6582278 0.892133 0.537648125
## 1431 12.2362869 0.892133 0.541645907
## 1432 12.2362869 0.811030 0.544159879
## 1433 12.2362869 0.729927 0.546055148
## 1434 11.8143460 0.729927 0.548388034
## 1435 11.3924051 0.729927 0.554057950
## 1436 11.3924051 0.648824 0.559561459
## 1437 10.9704641 0.648824 0.560996594
## 1438 10.9704641 0.567721 0.563133283
## 1439 10.5485232 0.567721 0.571656626
## 1440 10.1265823 0.567721 0.582904268
## 1441 10.1265823 0.486618 0.595956975
## 1442 10.1265823 0.405515 0.605903376
## 1443 9.7046414 0.405515 0.609982735
## 1444 9.7046414 0.324412 0.613824439
## 1445 9.2827004 0.324412 0.620059109
## 1446 8.8607595 0.324412 0.625549032
## 1447 8.4388186 0.324412 0.629281798
## 1448 8.4388186 0.243309 0.633437982
## 1449 8.4388186 0.162206 0.634935276
## 1450 8.0168776 0.162206 0.637462729
## 1451 7.5949367 0.162206 0.639272407
## 1452 7.1729958 0.162206 0.641814723
## 1453 6.7510549 0.162206 0.649791827
## 1454 6.7510549 0.081103 0.658624171
## 1455 6.3291139 0.081103 0.662777882
## 1456 6.3291139 0.000000 0.665001809
## 1457 5.9071730 0.000000 0.673153583
## 1458 5.4852321 0.000000 0.685306652
## 1459 5.0632911 0.000000 0.691532633
## 1460 4.6413502 0.000000 0.693086560
## 1461 4.2194093 0.000000 0.697569955
## 1462 3.7974684 0.000000 0.706977440
## 1463 3.3755274 0.000000 0.714337949
## 1464 2.9535865 0.000000 0.716377357
## 1465 2.5316456 0.000000 0.721248817
## 1466 2.1097046 0.000000 0.726826549
## 1467 1.6877637 0.000000 0.730600502
## 1468 1.2658228 0.000000 0.754031504
## 1469 0.8438819 0.000000 0.819082926
## 1470 0.4219409 0.000000 0.868008547
## 1471 0.0000000 0.000000 Inf
head(roc.df)
## tpp fpp thresholds
## 1 100 100.00000 -Inf
## 2 100 99.91890 0.002818221
## 3 100 99.83779 0.003621546
## 4 100 99.75669 0.004351793
## 5 100 99.67559 0.004477370
## 6 100 99.59448 0.004686418
## head() will show us the values for the upper right-hand corner of the ROC graph, when the threshold is so low
## Thus TPP = 100% and FPP = 100%
tail(roc.df)
## tpp fpp thresholds
## 1466 2.1097046 0 0.7268265
## 1467 1.6877637 0 0.7306005
## 1468 1.2658228 0 0.7540315
## 1469 0.8438819 0 0.8190829
## 1470 0.4219409 0 0.8680085
## 1471 0.0000000 0 Inf
## tail() will show us the values for the lower left-hand corner
## of the ROC graph, when the threshold is so high (infinity)
## that every single sample is called "not obese".
## Thus, TPP = 0% and FPP = 0%
## now let's look at the thresholds between TPP 60% and 80%
roc.df[roc.df$tpp > 60 & roc.df$tpp < 80,]
## tpp fpp thresholds
## 768 79.74684 41.68694 0.1215026
## 769 79.32489 41.68694 0.1216966
## 770 79.32489 41.60584 0.1217433
## 771 79.32489 41.52474 0.1220203
## 772 79.32489 41.44363 0.1224855
## 773 79.32489 41.36253 0.1230788
## 774 78.90295 41.36253 0.1235929
## 775 78.48101 41.36253 0.1237396
## 776 78.48101 41.28143 0.1238344
## 777 78.48101 41.20032 0.1240596
## 778 78.48101 41.11922 0.1242628
## 779 78.48101 41.03812 0.1244492
## 780 78.48101 40.95702 0.1245911
## 781 78.48101 40.87591 0.1247357
## 782 78.48101 40.79481 0.1248664
## 783 78.48101 40.71371 0.1249530
## 784 78.05907 40.71371 0.1252784
## 785 78.05907 40.63260 0.1255647
## 786 78.05907 40.55150 0.1258810
## 787 78.05907 40.47040 0.1263498
## 788 78.05907 40.38929 0.1268282
## 789 78.05907 40.30819 0.1271558
## 790 78.05907 40.22709 0.1273679
## 791 78.05907 40.14599 0.1281142
## 792 78.05907 40.06488 0.1288617
## 793 77.63713 40.06488 0.1290958
## 794 77.63713 39.98378 0.1292349
## 795 77.63713 39.90268 0.1294645
## 796 77.63713 39.82157 0.1296740
## 797 77.63713 39.74047 0.1297654
## 798 77.21519 39.74047 0.1298823
## 799 77.21519 39.65937 0.1300752
## 800 77.21519 39.57826 0.1303103
## 801 77.21519 39.49716 0.1306778
## 802 77.21519 39.41606 0.1311209
## 803 77.21519 39.33496 0.1314675
## 804 77.21519 39.25385 0.1317315
## 805 77.21519 39.17275 0.1318703
## 806 77.21519 39.09165 0.1319028
## 807 77.21519 39.01054 0.1320218
## 808 77.21519 38.92944 0.1322112
## 809 77.21519 38.84834 0.1323845
## 810 77.21519 38.76723 0.1327692
## 811 76.79325 38.76723 0.1333540
## 812 76.79325 38.68613 0.1337036
## 813 76.79325 38.60503 0.1337703
## 814 76.79325 38.52393 0.1339491
## 815 76.79325 38.44282 0.1341405
## 816 76.79325 38.36172 0.1342986
## 817 76.79325 38.28062 0.1345215
## 818 76.79325 38.19951 0.1347294
## 819 76.79325 38.11841 0.1349448
## 820 76.79325 38.03731 0.1351570
## 821 76.37131 38.03731 0.1353255
## 822 76.37131 37.95620 0.1353751
## 823 76.37131 37.87510 0.1354493
## 824 76.37131 37.79400 0.1355522
## 825 76.37131 37.71290 0.1357181
## 826 76.37131 37.63179 0.1361949
## 827 76.37131 37.55069 0.1366523
## 828 75.94937 37.55069 0.1367664
## 829 75.94937 37.46959 0.1370097
## 830 75.94937 37.38848 0.1374947
## 831 75.94937 37.30738 0.1377464
## 832 75.94937 37.22628 0.1377601
## 833 75.94937 37.14517 0.1378680
## 834 75.94937 37.06407 0.1380063
## 835 75.94937 36.98297 0.1382600
## 836 75.94937 36.90187 0.1385157
## 837 75.94937 36.82076 0.1385933
## 838 75.94937 36.73966 0.1386624
## 839 75.94937 36.65856 0.1387687
## 840 75.94937 36.57745 0.1389809
## 841 75.94937 36.49635 0.1391364
## 842 75.94937 36.41525 0.1398163
## 843 75.94937 36.33414 0.1405418
## 844 75.94937 36.25304 0.1407257
## 845 75.94937 36.17194 0.1409509
## 846 75.94937 36.09084 0.1411359
## 847 75.94937 36.00973 0.1413032
## 848 75.94937 35.92863 0.1414178
## 849 75.94937 35.84753 0.1416991
## 850 75.94937 35.76642 0.1421897
## 851 75.94937 35.68532 0.1426199
## 852 75.94937 35.60422 0.1428990
## 853 75.94937 35.52311 0.1431804
## 854 75.94937 35.44201 0.1434359
## 855 75.94937 35.36091 0.1435171
## 856 75.94937 35.27981 0.1435789
## 857 75.94937 35.19870 0.1438956
## 858 75.52743 35.19870 0.1442596
## 859 75.10549 35.19870 0.1443618
## 860 75.10549 35.11760 0.1444581
## 861 74.68354 35.11760 0.1446927
## 862 74.68354 35.03650 0.1449142
## 863 74.68354 34.95539 0.1453406
## 864 74.68354 34.87429 0.1463752
## 865 74.68354 34.79319 0.1470705
## 866 74.68354 34.71208 0.1471562
## 867 74.68354 34.63098 0.1472997
## 868 74.68354 34.54988 0.1473914
## 869 74.68354 34.46878 0.1477319
## 870 74.68354 34.38767 0.1480880
## 871 74.68354 34.30657 0.1482481
## 872 74.68354 34.22547 0.1484084
## 873 74.68354 34.14436 0.1485326
## 874 74.68354 34.06326 0.1489095
## 875 74.68354 33.98216 0.1492996
## 876 74.26160 33.98216 0.1498014
## 877 74.26160 33.90105 0.1504314
## 878 74.26160 33.81995 0.1507122
## 879 74.26160 33.73885 0.1507918
## 880 74.26160 33.65775 0.1510232
## 881 74.26160 33.57664 0.1512607
## 882 74.26160 33.49554 0.1513779
## 883 73.83966 33.49554 0.1516058
## 884 73.83966 33.41444 0.1517887
## 885 73.83966 33.33333 0.1519324
## 886 73.83966 33.25223 0.1520843
## 887 73.83966 33.17113 0.1524463
## 888 73.83966 33.09002 0.1527914
## 889 73.83966 33.00892 0.1529992
## 890 73.83966 32.92782 0.1531871
## 891 73.41772 32.92782 0.1532239
## 892 73.41772 32.84672 0.1532852
## 893 73.41772 32.76561 0.1533968
## 894 73.41772 32.68451 0.1534865
## 895 73.41772 32.60341 0.1536753
## 896 73.41772 32.52230 0.1538731
## 897 72.99578 32.52230 0.1538962
## 898 72.99578 32.44120 0.1539170
## 899 72.99578 32.36010 0.1540814
## 900 72.99578 32.27899 0.1543288
## 901 72.99578 32.19789 0.1545623
## 902 72.99578 32.11679 0.1548741
## 903 72.99578 32.03569 0.1550585
## 904 72.99578 31.95458 0.1552628
## 905 72.99578 31.87348 0.1555425
## 906 72.99578 31.79238 0.1557211
## 907 72.99578 31.71127 0.1558620
## 908 72.99578 31.63017 0.1560960
## 909 72.99578 31.54907 0.1562939
## 910 72.99578 31.46796 0.1565625
## 911 72.99578 31.38686 0.1568253
## 912 72.99578 31.30576 0.1569669
## 913 72.99578 31.22466 0.1572821
## 914 72.99578 31.14355 0.1575429
## 915 72.99578 31.06245 0.1578925
## 916 72.99578 30.98135 0.1582871
## 917 72.99578 30.90024 0.1584571
## 918 72.99578 30.81914 0.1585620
## 919 72.57384 30.81914 0.1587346
## 920 72.57384 30.73804 0.1589356
## 921 72.57384 30.65693 0.1591014
## 922 72.57384 30.57583 0.1591946
## 923 72.57384 30.49473 0.1593044
## 924 72.15190 30.49473 0.1601051
## 925 72.15190 30.41363 0.1610746
## 926 72.15190 30.33252 0.1614941
## 927 72.15190 30.25142 0.1618105
## 928 72.15190 30.17032 0.1620250
## 929 72.15190 30.08921 0.1621378
## 930 72.15190 30.00811 0.1623661
## 931 72.15190 29.92701 0.1625867
## 932 72.15190 29.84590 0.1628249
## 933 72.15190 29.76480 0.1633273
## 934 71.72996 29.76480 0.1636436
## 935 71.72996 29.68370 0.1638106
## 936 71.72996 29.60260 0.1641155
## 937 71.72996 29.52149 0.1645080
## 938 71.30802 29.52149 0.1648037
## 939 71.30802 29.44039 0.1649046
## 940 71.30802 29.35929 0.1650384
## 941 71.30802 29.27818 0.1651177
## 942 71.30802 29.19708 0.1652410
## 943 71.30802 29.11598 0.1653859
## 944 71.30802 29.03487 0.1655688
## 945 71.30802 28.95377 0.1657888
## 946 71.30802 28.87267 0.1660482
## 947 71.30802 28.79157 0.1663471
## 948 71.30802 28.71046 0.1665050
## 949 71.30802 28.62936 0.1668400
## 950 71.30802 28.54826 0.1671231
## 951 71.30802 28.46715 0.1671910
## 952 71.30802 28.38605 0.1674840
## 953 71.30802 28.30495 0.1682153
## 954 71.30802 28.22384 0.1688558
## 955 71.30802 28.14274 0.1690192
## 956 71.30802 28.06164 0.1690818
## 957 71.30802 27.98054 0.1692104
## 958 70.88608 27.98054 0.1694475
## 959 70.88608 27.89943 0.1696511
## 960 70.88608 27.81833 0.1698927
## 961 70.88608 27.73723 0.1701663
## 962 70.88608 27.65612 0.1703878
## 963 70.88608 27.57502 0.1705822
## 964 70.46414 27.57502 0.1706640
## 965 70.46414 27.49392 0.1708701
## 966 70.46414 27.41281 0.1711357
## 967 70.04219 27.41281 0.1715465
## 968 69.62025 27.41281 0.1719456
## 969 69.19831 27.41281 0.1720476
## 970 69.19831 27.33171 0.1723069
## 971 69.19831 27.25061 0.1727567
## 972 68.77637 27.25061 0.1730314
## 973 68.77637 27.16951 0.1730891
## 974 68.77637 27.08840 0.1732019
## 975 68.77637 27.00730 0.1733465
## 976 68.77637 26.92620 0.1737361
## 977 68.77637 26.84509 0.1742171
## 978 68.77637 26.76399 0.1745525
## 979 68.77637 26.68289 0.1747723
## 980 68.77637 26.60178 0.1747905
## 981 68.77637 26.52068 0.1748744
## 982 68.35443 26.52068 0.1750210
## 983 68.35443 26.43958 0.1751296
## 984 68.35443 26.35848 0.1752680
## 985 68.35443 26.27737 0.1754265
## 986 67.93249 26.27737 0.1755625
## 987 67.93249 26.19627 0.1759703
## 988 67.93249 26.11517 0.1764542
## 989 67.93249 26.03406 0.1769036
## 990 67.93249 25.95296 0.1775799
## 991 67.93249 25.87186 0.1779609
## 992 67.93249 25.79075 0.1784396
## 993 67.93249 25.70965 0.1789201
## 994 67.93249 25.62855 0.1792671
## 995 67.93249 25.54745 0.1804118
## 996 67.93249 25.46634 0.1813254
## 997 67.93249 25.38524 0.1814454
## 998 67.93249 25.30414 0.1814748
## 999 67.93249 25.22303 0.1815423
## 1000 67.93249 25.14193 0.1818132
## 1001 67.93249 25.06083 0.1826510
## 1002 67.93249 24.97972 0.1833137
## 1003 67.93249 24.89862 0.1834208
## 1004 67.51055 24.89862 0.1838345
## 1005 67.51055 24.81752 0.1844737
## 1006 67.51055 24.73642 0.1847850
## 1007 67.08861 24.73642 0.1851455
## 1008 67.08861 24.65531 0.1855256
## 1009 67.08861 24.57421 0.1858910
## 1010 67.08861 24.49311 0.1863592
## 1011 66.66667 24.49311 0.1865579
## 1012 66.66667 24.41200 0.1866115
## 1013 66.66667 24.33090 0.1869162
## 1014 66.66667 24.24980 0.1872959
## 1015 66.66667 24.16869 0.1875299
## 1016 66.66667 24.08759 0.1879739
## 1017 66.66667 24.00649 0.1884755
## 1018 66.66667 23.92539 0.1887098
## 1019 66.66667 23.84428 0.1890449
## 1020 66.66667 23.76318 0.1894721
## 1021 66.66667 23.68208 0.1900128
## 1022 66.66667 23.60097 0.1904552
## 1023 66.66667 23.51987 0.1906149
## 1024 66.66667 23.43877 0.1909289
## 1025 66.24473 23.43877 0.1920462
## 1026 66.24473 23.35766 0.1931580
## 1027 66.24473 23.27656 0.1935197
## 1028 65.82278 23.27656 0.1937889
## 1029 65.82278 23.19546 0.1938765
## 1030 65.40084 23.19546 0.1941734
## 1031 65.40084 23.11436 0.1952241
## 1032 64.97890 23.11436 0.1960953
## 1033 64.97890 23.03325 0.1962597
## 1034 64.97890 22.95215 0.1965208
## 1035 64.97890 22.87105 0.1969533
## 1036 64.97890 22.78994 0.1973311
## 1037 64.55696 22.78994 0.1975079
## 1038 64.55696 22.70884 0.1975563
## 1039 64.55696 22.62774 0.1976185
## 1040 64.13502 22.62774 0.1978219
## 1041 64.13502 22.54663 0.1980545
## 1042 64.13502 22.46553 0.1982482
## 1043 63.71308 22.46553 0.1987278
## 1044 63.71308 22.38443 0.1991728
## 1045 63.29114 22.38443 0.1992756
## 1046 63.29114 22.30333 0.1993247
## 1047 63.29114 22.22222 0.1994292
## 1048 63.29114 22.14112 0.1995474
## 1049 62.86920 22.14112 0.1998631
## 1050 62.86920 22.06002 0.2002293
## 1051 62.86920 21.97891 0.2008926
## 1052 62.86920 21.89781 0.2016252
## 1053 62.86920 21.81671 0.2019528
## 1054 62.86920 21.73560 0.2021528
## 1055 62.86920 21.65450 0.2024251
## 1056 62.86920 21.57340 0.2029357
## 1057 62.86920 21.49230 0.2033949
## 1058 62.86920 21.41119 0.2038128
## 1059 62.86920 21.33009 0.2040750
## 1060 62.86920 21.24899 0.2046368
## 1061 62.86920 21.16788 0.2054478
## 1062 62.86920 21.08678 0.2058945
## 1063 62.86920 21.00568 0.2061142
## 1064 62.86920 20.92457 0.2062072
## 1065 62.86920 20.84347 0.2062707
## 1066 62.44726 20.84347 0.2065928
## 1067 62.44726 20.76237 0.2071588
## 1068 62.44726 20.68127 0.2074757
## 1069 62.44726 20.60016 0.2076472
## 1070 62.44726 20.51906 0.2079363
## 1071 62.44726 20.43796 0.2081334
## 1072 62.44726 20.35685 0.2082165
## 1073 62.02532 20.35685 0.2087215
## 1074 62.02532 20.27575 0.2092862
## 1075 62.02532 20.19465 0.2095074
## 1076 62.02532 20.11354 0.2097483
## 1077 62.02532 20.03244 0.2099402
## 1078 61.60338 20.03244 0.2105638
## 1079 61.60338 19.95134 0.2112853
## 1080 61.60338 19.87024 0.2115594
## 1081 61.60338 19.78913 0.2117213
## 1082 61.60338 19.70803 0.2118524
## 1083 61.60338 19.62693 0.2119554
## 1084 61.18143 19.62693 0.2125377
## 1085 61.18143 19.54582 0.2131951
## 1086 61.18143 19.46472 0.2133921
## 1087 61.18143 19.38362 0.2135711
## 1088 61.18143 19.30251 0.2137336
## 1089 61.18143 19.22141 0.2143687
## 1090 61.18143 19.14031 0.2152968
## 1091 60.75949 19.14031 0.2157448
## 1092 60.75949 19.05921 0.2158177
## 1093 60.33755 19.05921 0.2158925
## 1094 60.33755 18.97810 0.2160273
## 1095 60.33755 18.89700 0.2163190
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 76.91%
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 76.91%
roc(attrition_data$Attrition,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE, partial.auc=c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x=45)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE, partial.auc = c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x = 45)
##
## Data: logistic$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Partial area under the curve (specificity 100%-90%): 2.881%
# Lets do two roc plots to understand which model is better
roc(attrition_data$Attrition, logistic_simple$fitted.values, plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, print.auc=TRUE)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
##
## Call:
## roc.default(response = attrition_data$Attrition, predictor = logistic_simple$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE)
##
## Data: logistic_simple$fitted.values in 1233 controls (attrition_data$Attrition No) < 237 cases (attrition_data$Attrition Yes).
## Area under the curve: 64.27%
# Lets add the other graph
plot.roc(attrition_data$Attrition, logistic$fitted.values, percent=TRUE, col="#4daf4a", lwd=4, print.auc=TRUE, add=TRUE, print.auc.y=40)
## Setting levels: control = No, case = Yes
## Setting direction: controls < cases
legend("bottomright", legend=c("Simple", "Non Simple"), col=c("#377eb8", "#4daf4a"), lwd=4)
Inference: Not Attrited - Since we are aiming
to see how many have not Attrition, based on their background factors. *
The accuracy of the model is very less showcasing that it is not a well
performing model. However, such low accuracy is a clear indication of
model underfitting. * At 95% Confidence interval, model is not
significant.
attr <- read.csv("/Users/meet/Desktop/Attrition Data copy.csv")
features <- c("Education", "DistanceFromHome", "EnvironmentSatisfaction", "JobSatisfaction", "Age", "MonthlyIncome", "NumCompaniesWorked", "WorkLifeBalance", "YearsAtCompany")
head(attr)
## Sr.no Department MaritalStatus EducationField Attrition Education
## 1 1 Sales Single Life Sciences Yes 2
## 2 2 Research & Development Married Life Sciences No 1
## 3 3 Research & Development Single Other Yes 2
## 4 4 Research & Development Married Life Sciences No 4
## 5 5 Research & Development Married Medical No 1
## 6 6 Research & Development Single Life Sciences No 2
## DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age MonthlyIncome
## 1 1 2 4 41 5993
## 2 8 3 2 49 5130
## 3 2 4 3 37 2090
## 4 3 4 3 33 2909
## 5 2 1 2 27 3468
## 6 2 4 4 32 3068
## NumCompaniesWorked WorkLifeBalance YearsAtCompany
## 1 8 1 6
## 2 1 3 10
## 3 6 3 0
## 4 1 3 8
## 5 9 3 2
## 6 0 2 7
dim(attr)
## [1] 1470 14
str(attr)
## 'data.frame': 1470 obs. of 14 variables:
## $ Sr.no : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Department : chr "Sales" "Research & Development" "Research & Development" "Research & Development" ...
## $ MaritalStatus : chr "Single" "Married" "Single" "Married" ...
## $ EducationField : chr "Life Sciences" "Life Sciences" "Other" "Life Sciences" ...
## $ Attrition : chr "Yes" "No" "Yes" "No" ...
## $ Education : int 2 1 2 4 1 2 3 1 3 3 ...
## $ DistanceFromHome : int 1 8 2 3 2 2 3 24 23 27 ...
## $ EnvironmentSatisfaction: int 2 3 4 4 1 4 3 4 4 3 ...
## $ JobSatisfaction : int 4 2 3 3 2 4 1 3 3 3 ...
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
attr.data <- as.matrix(attr[,c(6:14)])
row.names(attr.data) <- attr$Sr.no
attr_raw <- cbind(attr.data, as.numeric(as.factor(attr$Attrition)) - 1)
# Map numeric values to categorical labels
#test_raw.df$Attrition <- ifelse(test_raw.df$Attrition == 0, "No", "Yes")
colnames(attr_raw)[9] <- "Attrition"
smp_size_raw <- floor(0.75 * nrow(attr_raw))
train_ind_raw <- sample(nrow(attr_raw), size = smp_size_raw)
train_raw.df <- as.data.frame(attr_raw[train_ind_raw, ])
test_raw.df <- as.data.frame(attr_raw[-train_ind_raw, ])
attr_raw.lda <- lda(formula = train_raw.df$Attrition ~ ., data = train_raw.df)
attr_raw.lda
## Call:
## lda(train_raw.df$Attrition ~ ., data = train_raw.df)
##
## Prior probabilities of groups:
## 0 1 2 3 4 5
## 0.034482759 0.117967332 0.083484574 0.097096189 0.072595281 0.127949183
## 6 7 8 9 10 11
## 0.055353902 0.058983666 0.048094374 0.055353902 0.084392015 0.020871143
## 12 13 14 15 16 17
## 0.009981851 0.012704174 0.012704174 0.015426497 0.007259528 0.005444646
## 18 19 20 21 22 23
## 0.005444646 0.009074410 0.019963702 0.008166969 0.009981851 0.001814882
## 24 25 26 27 29 31
## 0.003629764 0.003629764 0.003629764 0.001814882 0.001814882 0.002722323
## 32 33 36 37 40
## 0.002722323 0.002722323 0.000907441 0.000907441 0.000907441
##
## Group means:
## Education DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age
## 0 2.842105 8.842105 2.710526 2.394737 32.52632
## 1 2.823077 9.776923 2.692308 2.746154 35.25385
## 2 2.750000 9.260870 2.695652 2.750000 34.59783
## 3 2.953271 7.738318 2.654206 2.551402 35.14019
## 4 2.612500 9.137500 2.662500 2.587500 36.96250
## 5 2.858156 8.900709 2.687943 2.702128 36.01418
## 6 2.836066 9.573770 2.737705 3.000000 34.86885
## 7 3.061538 8.230769 3.000000 2.753846 36.12308
## 8 3.018868 10.056604 2.679245 2.698113 37.13208
## 9 2.934426 9.672131 2.803279 2.868852 39.40984
## 10 3.021505 11.268817 2.559140 2.903226 37.17204
## 11 2.826087 7.652174 2.913043 2.782609 34.69565
## 12 2.636364 12.181818 2.727273 3.181818 42.63636
## 13 3.071429 7.428571 2.642857 2.785714 38.21429
## 14 3.500000 6.500000 2.785714 3.214286 39.85714
## 15 3.411765 9.411765 2.529412 2.647059 38.17647
## 16 3.375000 6.375000 2.625000 2.375000 40.12500
## 17 3.000000 12.666667 3.000000 2.833333 41.66667
## 18 3.333333 7.333333 2.333333 2.500000 40.83333
## 19 3.100000 8.300000 2.600000 2.500000 44.50000
## 20 2.727273 13.000000 2.818182 2.772727 43.04545
## 21 2.444444 12.111111 2.888889 2.444444 40.66667
## 22 2.818182 6.454545 2.909091 3.000000 43.45455
## 23 2.000000 5.000000 3.000000 3.000000 46.00000
## 24 3.000000 6.000000 1.750000 1.500000 47.75000
## 25 2.750000 11.000000 2.000000 2.750000 45.75000
## 26 2.750000 3.250000 2.750000 2.000000 47.00000
## 27 3.000000 18.000000 2.000000 3.000000 50.00000
## 29 3.000000 8.000000 2.500000 1.500000 55.50000
## 31 4.000000 7.333333 3.000000 2.000000 52.33333
## 32 3.000000 9.000000 1.666667 3.333333 50.66667
## 33 4.333333 1.666667 2.333333 3.333333 52.33333
## 36 3.000000 1.000000 4.000000 1.000000 55.00000
## 37 4.000000 10.000000 4.000000 3.000000 58.00000
## 40 4.000000 23.000000 4.000000 4.000000 58.00000
## MonthlyIncome NumCompaniesWorked WorkLifeBalance V10
## 0 4450.500 3.1842105 2.736842 0.36842105
## 1 4912.938 2.7846154 2.769231 0.33846154
## 2 4922.174 3.5108696 2.695652 0.22826087
## 3 5224.570 2.9158879 2.822430 0.15887850
## 4 5409.050 3.0250000 2.650000 0.16250000
## 5 5500.050 2.6808511 2.751773 0.08510638
## 6 5453.557 2.3934426 2.672131 0.09836066
## 7 6608.954 2.9692308 2.707692 0.13846154
## 8 6878.226 2.8490566 2.867925 0.09433962
## 9 7182.328 1.6557377 2.754098 0.11475410
## 10 6824.817 1.7311828 2.688172 0.13978495
## 11 6126.913 2.0869565 2.826087 0.04347826
## 12 9306.818 3.3636364 2.727273 0.00000000
## 13 7445.286 3.2857143 2.571429 0.14285714
## 14 10309.571 2.2142857 2.714286 0.14285714
## 15 7274.647 1.7647059 2.941176 0.05882353
## 16 9287.125 3.0000000 2.750000 0.12500000
## 17 10512.167 2.6666667 3.166667 0.16666667
## 18 10297.667 3.1666667 2.833333 0.16666667
## 19 11989.700 2.8000000 2.900000 0.10000000
## 20 11038.091 2.3636364 2.772727 0.04545455
## 21 17007.333 1.1111111 2.666667 0.11111111
## 22 17151.545 2.9090909 2.727273 0.09090909
## 23 11842.000 5.0000000 1.500000 0.50000000
## 24 13302.250 3.0000000 3.000000 0.25000000
## 25 16478.000 1.2500000 3.000000 0.00000000
## 26 14692.500 3.5000000 2.000000 0.00000000
## 27 17893.000 2.5000000 2.500000 0.00000000
## 29 19706.500 4.5000000 1.500000 0.00000000
## 31 18890.667 3.0000000 3.000000 0.33333333
## 32 17485.333 1.0000000 3.000000 0.33333333
## 33 16412.000 0.3333333 3.333333 0.33333333
## 36 19045.000 0.0000000 3.000000 0.00000000
## 37 13872.000 0.0000000 2.000000 0.00000000
## 40 10312.000 1.0000000 2.000000 1.00000000
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3 LD4
## Education 0.0194664362 -3.303152e-01 -9.372866e-02 6.458836e-01
## DistanceFromHome 0.0076650599 -2.944635e-02 -7.391267e-03 -7.226622e-02
## EnvironmentSatisfaction -0.0155544511 4.744783e-02 -8.609406e-02 1.871747e-02
## JobSatisfaction 0.0029752310 -3.084476e-01 -1.470254e-01 -2.040139e-01
## Age 0.0293813926 -3.814864e-02 -4.016911e-02 -4.090181e-02
## MonthlyIncome 0.0002248072 9.192477e-05 2.145038e-05 3.312454e-05
## NumCompaniesWorked -0.2065904930 2.979431e-01 4.222096e-02 -1.301104e-02
## WorkLifeBalance 0.0209949570 -3.451268e-01 -1.770520e-01 5.789019e-01
## V10 0.1722172408 4.552581e-01 -2.784967e+00 1.052412e-01
## LD5 LD6 LD7 LD8
## Education 0.1521563258 2.727383e-01 -1.445411e-01 2.574035e-02
## DistanceFromHome 0.0112006396 -5.000829e-02 5.317659e-03 -3.306848e-02
## EnvironmentSatisfaction 0.3582526472 4.207622e-01 4.121939e-01 -6.001451e-01
## JobSatisfaction 0.5396455021 1.311839e-01 -5.265080e-01 7.304698e-02
## Age -0.0907217560 4.596495e-02 -2.713211e-02 -3.151100e-02
## MonthlyIncome 0.0001036935 -5.908247e-05 1.784344e-05 2.449303e-05
## NumCompaniesWorked 0.0506937902 -1.808884e-02 -2.157988e-01 -1.121515e-01
## WorkLifeBalance -0.1335413466 -8.710694e-01 -2.342870e-01 -7.216141e-01
## V10 0.2069858973 -1.275450e-01 2.834566e-01 2.136920e-01
## LD9
## Education -6.005750e-01
## DistanceFromHome -7.203445e-02
## EnvironmentSatisfaction 7.666822e-02
## JobSatisfaction 2.871335e-01
## Age 2.661540e-02
## MonthlyIncome -1.908564e-05
## NumCompaniesWorked -8.334661e-02
## WorkLifeBalance 4.558913e-01
## V10 2.105454e-01
##
## Proportion of trace:
## LD1 LD2 LD3 LD4 LD5 LD6 LD7 LD8 LD9
## 0.6192 0.0976 0.0835 0.0650 0.0405 0.0383 0.0221 0.0187 0.0151
summary(attr_raw.lda)
## Length Class Mode
## prior 35 -none- numeric
## counts 35 -none- numeric
## means 315 -none- numeric
## scaling 81 -none- numeric
## lev 35 -none- character
## svd 9 -none- numeric
## N 1 -none- numeric
## call 3 -none- call
## terms 3 terms call
## xlevels 0 -none- list
print(attr_raw.lda)
## Call:
## lda(train_raw.df$Attrition ~ ., data = train_raw.df)
##
## Prior probabilities of groups:
## 0 1 2 3 4 5
## 0.034482759 0.117967332 0.083484574 0.097096189 0.072595281 0.127949183
## 6 7 8 9 10 11
## 0.055353902 0.058983666 0.048094374 0.055353902 0.084392015 0.020871143
## 12 13 14 15 16 17
## 0.009981851 0.012704174 0.012704174 0.015426497 0.007259528 0.005444646
## 18 19 20 21 22 23
## 0.005444646 0.009074410 0.019963702 0.008166969 0.009981851 0.001814882
## 24 25 26 27 29 31
## 0.003629764 0.003629764 0.003629764 0.001814882 0.001814882 0.002722323
## 32 33 36 37 40
## 0.002722323 0.002722323 0.000907441 0.000907441 0.000907441
##
## Group means:
## Education DistanceFromHome EnvironmentSatisfaction JobSatisfaction Age
## 0 2.842105 8.842105 2.710526 2.394737 32.52632
## 1 2.823077 9.776923 2.692308 2.746154 35.25385
## 2 2.750000 9.260870 2.695652 2.750000 34.59783
## 3 2.953271 7.738318 2.654206 2.551402 35.14019
## 4 2.612500 9.137500 2.662500 2.587500 36.96250
## 5 2.858156 8.900709 2.687943 2.702128 36.01418
## 6 2.836066 9.573770 2.737705 3.000000 34.86885
## 7 3.061538 8.230769 3.000000 2.753846 36.12308
## 8 3.018868 10.056604 2.679245 2.698113 37.13208
## 9 2.934426 9.672131 2.803279 2.868852 39.40984
## 10 3.021505 11.268817 2.559140 2.903226 37.17204
## 11 2.826087 7.652174 2.913043 2.782609 34.69565
## 12 2.636364 12.181818 2.727273 3.181818 42.63636
## 13 3.071429 7.428571 2.642857 2.785714 38.21429
## 14 3.500000 6.500000 2.785714 3.214286 39.85714
## 15 3.411765 9.411765 2.529412 2.647059 38.17647
## 16 3.375000 6.375000 2.625000 2.375000 40.12500
## 17 3.000000 12.666667 3.000000 2.833333 41.66667
## 18 3.333333 7.333333 2.333333 2.500000 40.83333
## 19 3.100000 8.300000 2.600000 2.500000 44.50000
## 20 2.727273 13.000000 2.818182 2.772727 43.04545
## 21 2.444444 12.111111 2.888889 2.444444 40.66667
## 22 2.818182 6.454545 2.909091 3.000000 43.45455
## 23 2.000000 5.000000 3.000000 3.000000 46.00000
## 24 3.000000 6.000000 1.750000 1.500000 47.75000
## 25 2.750000 11.000000 2.000000 2.750000 45.75000
## 26 2.750000 3.250000 2.750000 2.000000 47.00000
## 27 3.000000 18.000000 2.000000 3.000000 50.00000
## 29 3.000000 8.000000 2.500000 1.500000 55.50000
## 31 4.000000 7.333333 3.000000 2.000000 52.33333
## 32 3.000000 9.000000 1.666667 3.333333 50.66667
## 33 4.333333 1.666667 2.333333 3.333333 52.33333
## 36 3.000000 1.000000 4.000000 1.000000 55.00000
## 37 4.000000 10.000000 4.000000 3.000000 58.00000
## 40 4.000000 23.000000 4.000000 4.000000 58.00000
## MonthlyIncome NumCompaniesWorked WorkLifeBalance V10
## 0 4450.500 3.1842105 2.736842 0.36842105
## 1 4912.938 2.7846154 2.769231 0.33846154
## 2 4922.174 3.5108696 2.695652 0.22826087
## 3 5224.570 2.9158879 2.822430 0.15887850
## 4 5409.050 3.0250000 2.650000 0.16250000
## 5 5500.050 2.6808511 2.751773 0.08510638
## 6 5453.557 2.3934426 2.672131 0.09836066
## 7 6608.954 2.9692308 2.707692 0.13846154
## 8 6878.226 2.8490566 2.867925 0.09433962
## 9 7182.328 1.6557377 2.754098 0.11475410
## 10 6824.817 1.7311828 2.688172 0.13978495
## 11 6126.913 2.0869565 2.826087 0.04347826
## 12 9306.818 3.3636364 2.727273 0.00000000
## 13 7445.286 3.2857143 2.571429 0.14285714
## 14 10309.571 2.2142857 2.714286 0.14285714
## 15 7274.647 1.7647059 2.941176 0.05882353
## 16 9287.125 3.0000000 2.750000 0.12500000
## 17 10512.167 2.6666667 3.166667 0.16666667
## 18 10297.667 3.1666667 2.833333 0.16666667
## 19 11989.700 2.8000000 2.900000 0.10000000
## 20 11038.091 2.3636364 2.772727 0.04545455
## 21 17007.333 1.1111111 2.666667 0.11111111
## 22 17151.545 2.9090909 2.727273 0.09090909
## 23 11842.000 5.0000000 1.500000 0.50000000
## 24 13302.250 3.0000000 3.000000 0.25000000
## 25 16478.000 1.2500000 3.000000 0.00000000
## 26 14692.500 3.5000000 2.000000 0.00000000
## 27 17893.000 2.5000000 2.500000 0.00000000
## 29 19706.500 4.5000000 1.500000 0.00000000
## 31 18890.667 3.0000000 3.000000 0.33333333
## 32 17485.333 1.0000000 3.000000 0.33333333
## 33 16412.000 0.3333333 3.333333 0.33333333
## 36 19045.000 0.0000000 3.000000 0.00000000
## 37 13872.000 0.0000000 2.000000 0.00000000
## 40 10312.000 1.0000000 2.000000 1.00000000
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3 LD4
## Education 0.0194664362 -3.303152e-01 -9.372866e-02 6.458836e-01
## DistanceFromHome 0.0076650599 -2.944635e-02 -7.391267e-03 -7.226622e-02
## EnvironmentSatisfaction -0.0155544511 4.744783e-02 -8.609406e-02 1.871747e-02
## JobSatisfaction 0.0029752310 -3.084476e-01 -1.470254e-01 -2.040139e-01
## Age 0.0293813926 -3.814864e-02 -4.016911e-02 -4.090181e-02
## MonthlyIncome 0.0002248072 9.192477e-05 2.145038e-05 3.312454e-05
## NumCompaniesWorked -0.2065904930 2.979431e-01 4.222096e-02 -1.301104e-02
## WorkLifeBalance 0.0209949570 -3.451268e-01 -1.770520e-01 5.789019e-01
## V10 0.1722172408 4.552581e-01 -2.784967e+00 1.052412e-01
## LD5 LD6 LD7 LD8
## Education 0.1521563258 2.727383e-01 -1.445411e-01 2.574035e-02
## DistanceFromHome 0.0112006396 -5.000829e-02 5.317659e-03 -3.306848e-02
## EnvironmentSatisfaction 0.3582526472 4.207622e-01 4.121939e-01 -6.001451e-01
## JobSatisfaction 0.5396455021 1.311839e-01 -5.265080e-01 7.304698e-02
## Age -0.0907217560 4.596495e-02 -2.713211e-02 -3.151100e-02
## MonthlyIncome 0.0001036935 -5.908247e-05 1.784344e-05 2.449303e-05
## NumCompaniesWorked 0.0506937902 -1.808884e-02 -2.157988e-01 -1.121515e-01
## WorkLifeBalance -0.1335413466 -8.710694e-01 -2.342870e-01 -7.216141e-01
## V10 0.2069858973 -1.275450e-01 2.834566e-01 2.136920e-01
## LD9
## Education -6.005750e-01
## DistanceFromHome -7.203445e-02
## EnvironmentSatisfaction 7.666822e-02
## JobSatisfaction 2.871335e-01
## Age 2.661540e-02
## MonthlyIncome -1.908564e-05
## NumCompaniesWorked -8.334661e-02
## WorkLifeBalance 4.558913e-01
## V10 2.105454e-01
##
## Proportion of trace:
## LD1 LD2 LD3 LD4 LD5 LD6 LD7 LD8 LD9
## 0.6192 0.0976 0.0835 0.0650 0.0405 0.0383 0.0221 0.0187 0.0151
plot(attr_raw.lda)
attr_raw.lda.predict <- predict(attr_raw.lda, newdata = test_raw.df)
attr_raw.lda.predict$class
## [1] 5 2 10 1 5 10 10 10 5 1 5 5 5 4 20 5 5 5 5 5 5 20 5 5 5
## [26] 1 22 1 5 5 5 10 10 5 3 2 10 3 5 5 5 1 5 5 5 5 2 10 1 2
## [51] 5 1 5 2 5 2 5 3 22 1 5 25 1 5 5 5 5 1 5 22 10 5 5 5 10
## [76] 5 5 5 5 10 5 10 10 5 5 5 5 5 7 1 1 5 2 22 5 1 2 5 5 10
## [101] 5 22 5 10 5 10 1 1 20 5 10 5 1 5 1 19 2 9 5 4 10 1 5 5 5
## [126] 5 3 5 5 10 5 1 5 5 3 5 10 1 5 2 5 10 5 31 10 1 5 5 3 5
## [151] 5 22 5 10 5 2 1 5 5 5 1 5 5 5 2 5 5 5 5 5 5 5 9 2 23
## [176] 1 10 5 2 3 5 3 5 21 5 5 25 2 5 10 5 9 5 1 2 23 5 0 5 5
## [201] 10 24 1 5 5 21 5 22 5 10 2 21 10 7 1 5 5 2 3 2 5 5 5 31 5
## [226] 5 5 5 1 1 1 5 3 5 5 5 5 5 20 5 10 5 1 10 10 22 10 5 9 5
## [251] 5 9 3 20 1 2 20 1 21 10 1 1 3 3 1 19 5 1 10 1 5 5 5 5 1
## [276] 5 5 10 5 3 5 5 5 5 3 1 5 5 5 5 1 3 27 5 5 5 5 5 10 5
## [301] 5 21 5 5 14 5 5 1 1 22 5 5 1 5 9 2 5 3 5 2 5 5 5 5 5
## [326] 10 3 1 5 3 20 1 5 22 1 1 3 10 1 3 5 5 5 1 3 5 1 5 5 5
## [351] 5 10 5 5 5 5 2 2 5 10 1 23 2 1 20 5 5 5
## 35 Levels: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ... 40
attr_raw.lda.predict$x
## LD1 LD2 LD3 LD4 LD5
## 4 -0.65994100 -1.046642637 0.208931611 1.322116351 0.5321769957
## 5 -2.38566231 2.803676303 1.493589535 -0.235567624 -0.5420505442
## 9 1.31494066 -1.185674452 0.053705581 -0.741404607 0.7858707433
## 15 -1.50199360 0.374639622 -2.200597756 -0.631552018 1.0289973231
## 20 -1.13087679 0.100842717 0.153265568 0.322215725 0.7649546796
## 23 1.69275294 -0.499279106 0.697160745 1.453958669 -0.2367840393
## 28 0.74233166 -1.214178053 0.085351502 0.920692161 -0.7708438262
## 29 0.98023242 -0.764332076 0.090629361 0.540044154 -0.0936780662
## 31 -1.38115968 -0.186912101 0.366924055 0.473054002 0.6594688426
## 34 -0.88979887 -0.682196127 -2.995393125 0.713135093 0.4872293001
## 44 0.49033317 -0.099940908 0.631495426 0.752997946 1.5835394609
## 45 -0.53608092 -0.467267958 0.494385746 0.111358845 0.7732914189
## 59 -0.44347372 -0.179239431 0.438653089 0.405489513 1.8447001393
## 64 0.09620365 0.685945991 0.179783751 -2.125551103 -2.9584129334
## 66 2.46200927 -0.315853376 -0.321672840 -0.205522758 -0.2807041467
## 68 1.05445874 0.154513555 0.445710147 0.479671757 -1.7022691884
## 75 -0.91836480 -0.714711139 0.272350867 0.073530757 0.0793615693
## 86 0.36736989 -0.381058302 -0.400774214 -1.231397858 -0.3853385473
## 93 -0.27071210 0.516541000 0.969012322 -0.236630708 -0.0146315138
## 96 0.69330162 2.091216969 0.551157484 -0.430154911 -0.6830066673
## 104 -0.13376734 -1.140816750 0.445626593 1.071200088 -0.4026831439
## 113 3.15177839 -0.879756084 -0.506401586 -1.584230545 0.8179742912
## 114 -0.66044653 -0.559303019 0.867841905 -1.360307254 0.2790157098
## 117 1.12908624 0.855789670 0.857164674 1.156010076 -0.1707350101
## 122 0.41462794 -1.030002433 0.339236250 -0.458275521 -0.3058009489
## 123 -0.89047229 0.993197406 -2.880188575 -0.177784023 -1.8618444984
## 124 2.41766785 1.682498330 0.425727353 0.139777731 -0.2657487958
## 128 -1.11023351 0.605853256 -1.722333824 -1.930503777 1.7711942264
## 129 -0.91085611 -0.295937134 0.827936875 -0.315854795 1.1531200711
## 134 0.35205684 0.496237025 0.408211104 -1.246188265 -0.2922256090
## 136 -1.13574502 1.301261574 0.827613309 -0.140322130 -0.8026756704
## 139 0.40538621 -0.464968364 0.862645248 -0.682568172 0.9559102788
## 140 0.23445626 -0.426107127 0.703518055 -0.888301216 1.4736697672
## 144 -0.68917893 -0.866256496 0.741690997 -0.929285017 -0.1497441614
## 152 0.40154184 -0.730180600 0.376848100 2.361309484 0.0373900475
## 154 -1.86694692 1.587048542 0.733113958 -1.349071358 -1.3338201877
## 155 0.73247183 -0.669023883 0.461647092 0.316049907 0.9812755189
## 160 -1.80804199 0.324597862 0.458809273 1.247249642 0.2551667145
## 173 -1.43903810 0.971475496 0.709011140 -0.533472690 -0.3834560679
## 174 -0.67531369 -0.194128379 0.762461292 0.760050508 -0.7012518365
## 177 -0.53290352 -1.723443738 0.021074023 1.104132603 0.3235671093
## 183 -0.10223029 -0.156617619 -2.334361975 -1.824821087 -1.1991691870
## 186 -0.63246252 -0.745854066 0.365099841 0.080250165 -0.0522829017
## 194 -1.13507649 -1.050722628 -0.343599707 0.286842521 -0.0092374717
## 196 -0.27249857 -0.471619022 0.666281972 -0.974778953 -1.3755905553
## 198 0.04213953 -0.792314135 0.080676266 -1.592246245 -0.4502769323
## 199 -1.35422549 1.510579360 0.431410199 1.206491025 0.8507769908
## 200 -0.03185075 -0.386851491 0.273063945 -2.684004491 1.4733248873
## 205 -0.56813465 2.098876179 -1.887564028 -2.176516655 -0.9810294807
## 209 -1.63835726 1.125490634 0.376710740 -0.152660186 1.5327284867
## 214 1.22090923 1.095759464 0.496648770 -0.501350142 -0.8376169879
## 217 -0.38597952 1.300261374 -1.818213978 -0.228253191 0.5604029902
## 220 0.40645157 -0.323986499 -0.139603094 0.312712041 -2.2394384394
## 221 -1.34796757 1.765805798 0.591077606 0.554489070 -0.0286310119
## 229 0.72244115 -0.585789031 0.272274877 1.493918336 0.2940996320
## 231 -1.30271768 0.393038061 -0.077215639 -0.898298259 -0.7043772630
## 239 -0.68484849 0.275580148 0.726429492 0.205123403 -0.4114428682
## 241 -1.87516577 0.461336050 0.307597415 1.102028901 -0.1588452216
## 245 3.54574355 -0.271326739 0.081752203 0.659921289 1.0891354874
## 251 0.28260050 1.383834802 -2.072200877 0.227271651 0.2215028858
## 257 -0.29303902 -0.740314913 0.193581126 0.790954212 -1.6104277126
## 258 3.46777377 0.455347714 0.693168053 0.320610619 0.1699020626
## 260 -0.01782307 -0.949734786 -2.474339632 -0.865437388 -0.1155176122
## 270 -0.29103538 -1.497833786 -0.022810664 0.155696251 0.6616207743
## 278 0.12548651 0.027840179 0.776141551 -0.022045614 -2.0554331627
## 279 -0.14569038 0.881492846 1.260668933 0.250108829 0.7235391355
## 286 -0.75273370 -1.191465199 -0.007290639 0.426843136 0.4520452342
## 287 -0.42154810 0.010227386 -2.635432187 -2.361515170 0.2188817158
## 290 -0.71433261 -0.614086524 0.421854318 -0.317203922 1.3187029155
## 301 2.51079342 0.190828256 0.323124085 1.705312278 0.6145637434
## 305 1.19278369 -0.578774674 0.294131168 0.008798970 0.7726904525
## 307 -0.12024493 -0.214131036 0.545551025 -0.065536580 0.9160970789
## 310 -0.04842207 -1.507316483 0.212348094 1.113001296 1.0649828130
## 313 -0.59134733 -0.924155832 0.543022378 0.101573313 1.0780112185
## 316 -0.18941397 -2.329825912 -0.357389122 0.182475810 -0.2130138694
## 319 -0.94567333 0.020178810 0.929818734 0.369228985 0.1377037865
## 326 0.64506486 0.079725936 0.662687714 0.004243871 0.7215443125
## 329 -0.62726061 -0.221799437 0.575609533 -0.617273891 0.7003428471
## 336 0.32038772 0.063640517 0.471979685 -0.794142523 0.0493841298
## 338 -0.22989219 -2.003600594 0.237511221 1.505147800 0.9982374136
## 340 -0.02678249 -0.447619177 0.803096948 1.482251686 0.2190669322
## 342 1.69870098 -0.793305197 0.188190570 -0.966170749 0.9312300488
## 343 0.26132499 -0.709689895 0.466646290 0.453471062 1.5123955229
## 347 -0.75521583 0.975388737 0.384253358 0.374626260 -0.2744932280
## 350 -0.43442844 -0.029210568 0.685103617 0.390840964 1.0456750814
## 351 -0.28731183 -0.734559334 0.175291062 -0.924146507 -1.1830215772
## 352 -0.82504577 -0.437280073 0.571778366 0.956843091 -0.4942471564
## 357 0.10373767 -0.859506244 0.133555452 0.868336094 -0.3277430970
## 359 -0.34277848 -0.502963019 0.069425841 1.870798219 1.4697220899
## 364 -0.50489890 -0.325293600 -2.498333454 0.635020294 0.6033936237
## 367 1.22832154 0.162946463 -2.267474199 0.743375572 -1.0735620203
## 368 0.54936688 0.307722476 -0.205130022 -0.542714799 0.4959922892
## 373 -1.37905753 1.678705651 0.733019270 1.008198730 0.3021005711
## 380 2.86235676 -0.320137939 -0.297436526 0.068379181 0.0308135907
## 381 -0.54600859 -1.130365758 0.370642173 1.808022271 1.4336258413
## 383 -0.49221054 0.955847464 -1.671601873 0.184733850 -0.5504783893
## 386 -2.36214329 1.794218772 -2.105739456 0.484423720 1.3926109106
## 395 -0.42975219 0.913171901 1.297471189 -0.917848130 -0.9297433793
## 397 -0.56940474 -0.580704583 0.017640600 0.547446439 -0.3579510371
## 399 -0.39018663 -1.534817294 0.081582261 0.202090611 0.1124306350
## 400 -0.93425904 0.302553043 0.770738302 0.641823975 -0.7640366318
## 401 3.13538701 1.176678859 0.785457350 -0.214315297 0.4814305454
## 405 -0.35815889 0.113513569 0.909273291 -0.332936193 -0.4282710010
## 410 -0.02481941 -1.187955227 0.178525927 -2.231296267 -1.1506957977
## 413 0.03285411 -0.883583817 0.015737049 -1.487144804 -0.6082487427
## 419 -0.72929789 -0.800865569 0.900886063 -1.901511116 0.9686710569
## 422 -1.29154440 -0.342647973 -2.454530733 1.347121550 0.6343152395
## 423 -0.95258614 -0.194858751 -1.892014984 1.087789522 0.9893261447
## 428 1.37025093 -0.688058850 -0.479121097 -1.061895213 -2.4455813433
## 429 -0.58611440 0.048983959 0.167907562 -0.710638354 -1.1616965174
## 431 0.02855233 -1.528615766 0.068002970 -0.721860535 0.4976746255
## 435 1.04224460 0.471201001 0.748180158 0.053221018 0.0953998250
## 436 0.76408073 2.377528233 -1.905542307 -0.559621462 0.9808417739
## 439 -0.07900580 0.152562873 0.354208598 -0.227617677 0.9860112167
## 441 -0.36920540 2.664642095 -1.715262510 -0.205017818 0.0601575191
## 446 2.88206461 -0.615788408 -0.090918948 0.567298635 -1.2125159782
## 447 -0.90015023 0.887167524 0.200834253 -0.974802471 0.7686691107
## 453 0.31634894 -1.304997724 -0.203555369 1.116408285 -1.2471188156
## 465 -0.11183764 -0.243470765 0.229825594 1.107354540 0.3115361896
## 466 0.69048160 1.101514243 0.624677175 -2.666007094 -0.8841696107
## 468 0.87924589 -0.665156870 0.536308656 1.069036202 -0.7635256804
## 470 -1.49771473 1.462075992 -2.260881988 0.858610241 1.4607871996
## 472 0.67807041 0.070903161 0.368941205 0.150176793 0.4649918136
## 477 -1.03477006 -0.218360790 0.784684378 -0.435151170 0.5804352876
## 479 -1.02840023 -0.214601803 0.892306738 -1.075347435 0.1126803569
## 484 -0.86806148 -0.596124922 0.407922170 -1.914938698 -0.0101447889
## 494 -0.21268193 -0.718265371 0.055728388 1.602336379 -1.2254203288
## 495 -0.62434232 -1.156168865 0.260202659 -0.189246085 0.0200344487
## 502 -0.93768794 -0.725259186 0.491543639 0.752859820 0.2082824645
## 509 0.29600572 -1.271099397 0.211742355 0.905851613 0.5949781987
## 513 -0.77423373 -1.645908055 0.500448925 1.291752300 0.4011101232
## 515 -0.36778693 0.253837485 -1.920557077 1.147891063 -1.5215209346
## 518 -0.23594238 -0.369347593 0.733517883 0.923468927 0.7728313899
## 519 -0.02124878 -1.858698173 -0.186722398 0.674605900 0.7283555060
## 534 0.42963794 1.131594773 0.538193556 1.497875212 -0.1724448824
## 538 0.47431352 1.139662701 1.182981552 -0.206072855 0.5149822207
## 544 -0.17555202 -1.525288208 0.023225467 -1.333974774 -1.3239182651
## 548 -1.17123581 0.352930503 -2.668107735 -0.831643236 -0.1706167247
## 549 0.17180562 -0.805684387 -0.166760282 -0.700995930 0.6521300274
## 552 -1.40292456 2.709477416 1.061284083 -0.530500465 -0.0287216406
## 556 -0.88383485 -0.517667588 0.545495615 0.517718124 0.2182062503
## 559 0.06081980 -1.857038942 0.256621771 -0.335239942 0.5718641297
## 560 -1.54290357 0.655319445 0.490132123 0.617800493 0.7554221830
## 562 3.06429086 -0.265071442 -0.052020113 1.975182283 -1.3164082006
## 564 -0.04421590 -0.137856502 0.827756126 -2.643726075 1.7132123983
## 567 0.26410935 -0.051980014 -2.754666137 -2.132353974 -0.7691800090
## 572 -0.95632162 0.218766634 0.919264194 0.223202015 0.5576645325
## 575 -0.73499261 -1.097194680 0.258886787 1.183576280 0.3313582449
## 580 -0.29770444 -0.350584223 0.587873616 1.791550465 -0.8546522276
## 582 -0.98834084 0.137835935 0.542212197 0.948055602 0.8269850280
## 583 -0.18817231 -0.239886963 0.384352177 0.045820398 -1.1778559220
## 585 3.12567261 0.161650974 0.439327974 -0.359439435 1.1856363444
## 587 -0.93360395 -0.308431735 0.848342276 0.788926361 0.3435280610
## 591 1.56864981 -0.717347262 0.328293524 1.251263087 0.7929717120
## 597 -1.12028664 -0.505206663 0.219173349 1.345473903 0.3879313066
## 598 -1.39070297 1.694478879 0.308024807 -0.396895289 0.6611086719
## 599 -1.34954770 1.551604873 -1.861951398 1.090250674 1.3630692011
## 600 -1.29400726 -0.040821988 0.451591643 -0.048244984 -0.6053841981
## 602 -0.84971079 -0.148257871 0.347917436 0.047512299 -0.5519856878
## 604 -0.44613948 -1.297932661 -0.013410623 0.199208221 -1.5021917054
## 608 1.13046751 -1.371857574 -3.320343960 0.062261734 -0.2350592736
## 616 -1.14415862 -0.561341870 0.547896687 0.098878909 1.4727947811
## 622 0.12709476 -0.197165554 0.563493480 -0.659128670 0.2313383348
## 629 -0.29257637 -0.373367982 0.152299133 0.293466662 0.8221298747
## 631 -1.68987617 2.135568828 1.311241421 -0.740261140 2.4570915881
## 632 -0.49682471 -1.429595750 0.058692821 -0.344228312 -0.7700725335
## 633 -1.34242473 0.382622431 0.321581986 -1.217928655 -0.7669282940
## 634 -0.43310028 -0.853517754 0.643146295 0.538301055 -2.0996783477
## 639 -0.61231211 0.568189086 1.036065740 0.652244830 -0.6187271550
## 643 -0.25403402 -1.169059093 0.334245200 0.217385135 -1.3142657945
## 644 -0.10202828 -0.559041383 0.149287678 -0.429612730 0.1699291513
## 651 -0.44230125 0.135463847 0.129349042 -0.322322482 0.5507688903
## 652 0.29590691 -1.394831900 -0.226818406 -0.625803579 -0.7539288063
## 655 -1.43800977 1.072348659 0.266786817 0.284017714 0.9569680970
## 661 -1.60892001 1.846887472 -2.935238882 -2.365099347 -0.9726673134
## 663 -1.09671212 0.482473489 -1.708125663 0.759191563 1.4407825829
## 665 0.48486093 -0.464757079 0.441079045 -2.199991705 0.5722711757
## 672 -0.77078827 -0.829872719 0.510639036 0.266201140 -0.9818752442
## 673 -0.82438207 0.993520255 0.364519857 -1.119008974 -0.1736965275
## 676 -1.17950887 -0.985583358 0.326841581 1.611087752 -0.0503782214
## 687 -0.22655137 -0.028449494 0.334273489 0.587258076 -1.1528560619
## 693 0.19914095 -0.433388463 0.534048256 2.457633724 -0.5524918717
## 704 0.15947816 -1.215653923 0.048283198 -0.165546894 0.4720921857
## 711 2.69547651 0.207550282 0.510963770 0.145970855 2.0440145649
## 713 -0.89871624 -0.107702337 0.537457096 -1.587681035 0.1685477694
## 714 -0.87655199 -1.216834962 -0.334605429 0.724624497 -0.0041124163
## 717 3.17426927 0.129956124 0.414556686 0.972045604 0.2758245535
## 718 -2.39875941 1.434982895 0.922644799 0.706028230 0.7196060557
## 728 -1.50787235 -0.446814797 0.969450904 0.196349547 1.2415696589
## 730 1.24334588 -0.785575159 0.389558944 -0.699425106 1.1479598981
## 734 -0.33305252 -0.162369816 0.592915852 0.269812289 1.6571279251
## 739 1.65612266 0.369752493 0.327781631 -0.594713196 1.0682398356
## 740 -0.29136941 -1.415881861 0.554644916 1.436296274 0.6161686884
## 745 -0.75253444 1.900926407 -1.640019983 -1.606256554 -0.7892778085
## 748 -1.03664518 0.808159412 0.413567387 0.915989335 0.6663616442
## 759 1.65076649 0.390675748 0.023429430 -2.015885032 -1.0289691285
## 761 0.74425426 -0.466586225 -0.118975229 0.255651076 -1.8141702794
## 763 -1.90767245 1.919986192 -1.448891451 1.398154086 -0.7796240348
## 766 -0.93044361 -0.697036808 0.176734419 1.069952789 -0.1874218789
## 768 -0.72971398 0.490664621 0.576200724 0.151398608 -0.1633581231
## 769 0.92468500 -0.241668350 0.526372481 -1.280040228 -0.7324530134
## 775 1.82434699 2.419340912 0.367230538 -0.094286468 -1.7624496942
## 780 -1.63697291 0.547385980 -2.897082563 1.022680175 -1.7318317285
## 782 -0.64401249 0.510626077 1.267125318 0.847717931 -1.2050701934
## 794 -0.88594640 -0.410372984 0.928815263 -1.290644277 -0.1981286290
## 800 3.07578913 0.975490444 0.610609879 0.644323703 -0.1997156908
## 804 -1.00947441 -0.838365769 0.193774592 1.034779780 0.7314942195
## 805 2.72940877 -0.082960155 0.251497724 0.463990945 0.2472923512
## 807 0.41170370 0.804703586 0.150342843 0.594056369 -1.3172876925
## 808 1.07361729 -1.252887885 0.125297454 0.799186528 0.3526630210
## 812 -0.80355644 1.957127160 0.698568418 0.171193191 -0.0118213347
## 815 3.40522986 -0.163145994 0.207800610 0.708919072 1.1098255650
## 818 0.48103838 -1.307958127 0.235496338 0.003556732 0.4485899895
## 822 1.10806552 0.932554466 0.106429582 0.783549714 -0.0907301831
## 830 1.00042042 -0.102873754 -1.996262259 1.534703655 -0.8472450828
## 834 -0.91587929 -0.609786770 0.513564474 0.692588846 0.9195865319
## 835 -0.00227033 0.237556464 0.815009300 -1.613456169 -0.2399135963
## 838 0.32981769 2.116898285 0.797567546 0.232570044 0.8850290200
## 841 -1.79581031 0.365825368 0.340516536 1.298225890 0.5142966904
## 842 -2.07731502 1.465930854 0.966295624 -0.337515327 1.3182820581
## 844 -0.47628844 -1.091494960 0.633783639 1.398313855 0.7887977186
## 847 0.85437923 0.127663673 0.485983797 1.661844941 -0.0296666012
## 848 0.08246467 -0.152886319 0.581313790 1.281527398 -0.6106971943
## 852 3.22714052 1.123063457 0.063750322 1.242346699 -0.7041174037
## 853 -0.72887936 -0.374377453 0.658544904 -0.902821139 0.3183571246
## 854 -1.13487521 0.508021015 1.286895936 0.546862032 0.0906105371
## 856 0.20620607 -0.445638288 0.263263550 -0.007668919 1.0375865230
## 857 -1.00782105 -0.006213069 1.262852678 0.577009344 0.6310448967
## 858 -0.08924878 -1.262109830 -2.982961290 0.453751011 -0.5358248693
## 861 -0.59838811 -0.830735824 -2.238528819 1.665702145 1.8619944385
## 865 -1.49080026 2.285961543 -1.624374941 -1.233706105 -1.9851820120
## 871 0.46421302 0.186933274 0.619627404 0.792509269 -0.2005421380
## 879 -0.85217884 0.677720908 0.203534473 2.692411272 -0.7033115107
## 882 -0.88606950 0.767443009 0.615422026 0.173681199 0.6760825409
## 889 0.45483786 0.960013716 0.682069317 -1.006077978 1.3438226181
## 890 -0.90318228 -0.053624043 1.177298420 -0.122637299 -1.0428387731
## 892 -0.55504836 -0.979225266 0.147642998 -1.283100348 -1.5616611351
## 898 -0.21480956 -0.664381236 -0.585263280 -0.587062146 -1.3600222871
## 915 2.36164394 0.246902279 -0.054701057 -1.319318855 -1.2976107205
## 927 0.89836573 -0.842190459 -0.282726552 1.432235867 0.9028955767
## 939 0.15383688 -2.780992679 -0.696358093 -1.219693613 -2.6422954620
## 942 -0.10210854 -1.281028038 0.506881337 0.391892162 0.2781270505
## 947 1.06744431 -0.331299113 -2.697910125 -0.052933796 0.5029172221
## 949 1.40922283 0.005520471 0.885403691 1.102040326 0.0993222231
## 950 0.21095598 -1.347508097 0.295423358 -1.288369055 -1.1054064020
## 957 2.79678857 1.271941686 -0.033246027 0.715759657 -0.0417164927
## 959 0.84143231 -0.678466668 0.325878239 -0.382971903 1.5587461371
## 962 -0.27671702 -1.076654906 0.236039693 1.193715925 0.1426307585
## 963 2.37654896 -0.178968173 0.036417129 0.349009720 -0.9757072317
## 964 -0.05202251 0.936805092 0.839073836 0.374645296 -1.5182389123
## 965 0.17606724 -0.257566311 0.539601931 0.196993490 -0.9660564573
## 970 0.89351702 -1.167838344 -0.347277086 -0.048316201 0.0873673146
## 973 -1.40328805 -0.858097937 0.568059415 1.766184674 1.9899557311
## 977 1.88582136 -0.015829448 -0.270287429 -1.197276687 -0.7820752226
## 986 0.31327428 -0.428846938 -2.388936592 -0.334481707 1.6060376301
## 991 -0.08722510 1.278310508 0.686612293 -0.252849195 0.7762602911
## 995 2.14747079 -0.253606780 -0.110578827 -2.802912254 0.0403854504
## 998 -0.67247700 -0.822082738 -2.449545500 0.643982182 1.3869002335
## 1000 2.97744744 0.282549775 0.525269111 0.664674214 -0.4060054618
## 1003 0.73748506 -0.368766467 0.324890599 -1.157437589 1.1156511899
## 1007 0.07171399 -0.080456358 -2.549796337 -1.954094556 -2.6467646768
## 1008 0.68979198 0.001305969 -2.219013751 -1.197504450 1.3810396278
## 1014 -1.54252884 1.526471253 0.887362663 1.547661380 0.2679233933
## 1016 -1.45864394 0.790766647 0.648345894 1.784612501 -0.4484405491
## 1017 -0.83342692 -0.662518434 -2.246019545 1.174120663 -1.0943783920
## 1025 2.60396188 -0.132014135 0.125509862 1.790840655 -0.3773707061
## 1029 -0.76236911 -1.264750553 0.153754431 0.841001732 -0.6323979179
## 1032 0.98730990 -0.175104963 -2.833821286 0.333921665 -0.2964996952
## 1035 1.40746227 -0.124689720 0.373798250 -0.422457769 -1.4397983059
## 1040 -0.40323146 -0.963906142 -2.405852209 0.891174216 -0.3764297808
## 1043 -0.68163231 -0.623159779 0.021980481 0.045421347 -0.8261479802
## 1052 -1.12856729 0.423630012 0.416661483 1.011070427 -0.7802949220
## 1053 -1.10989171 -0.572284868 0.621677208 -0.141904758 0.3027383324
## 1056 1.37590754 2.842908407 1.372820084 -0.051249221 0.5274852616
## 1058 -0.73067948 1.907729298 -1.405985347 -0.744963864 0.2135030172
## 1060 -0.74244494 -0.296201648 0.369381869 -1.003130888 -0.1132981502
## 1062 -1.08656218 -0.109216336 0.812233111 -0.149199989 0.5258855408
## 1064 0.62513650 -0.557339849 0.553673590 -0.145962788 1.1560588264
## 1065 -0.72970395 -1.311183028 0.286645663 1.488675875 -0.0003241278
## 1067 -1.84587535 1.261015142 0.922322055 1.337407040 -0.6198380211
## 1068 -0.22424801 -0.526135477 0.042656337 -1.259247042 -0.7157881421
## 1071 -0.13231810 -0.189026900 0.854529470 1.059883026 -0.4035590729
## 1072 -0.41630149 0.639704934 0.300817697 -0.211528432 -2.3142022640
## 1080 0.15725942 0.576375766 0.602617453 0.522660943 -0.6678850398
## 1081 1.36917604 2.048308665 0.425881902 1.271337171 -0.0556553306
## 1084 -0.89748826 0.786027181 -2.188082361 -0.097864496 -0.6318971960
## 1091 0.32892044 1.740639547 1.224415767 -0.224524436 -0.1358199080
## 1092 -0.19654835 -0.925993525 0.317344293 -0.662871492 0.2331007588
## 1102 -0.46162870 0.770502287 0.716929013 0.203057096 0.2105954423
## 1103 -1.05468206 -0.570884667 0.290693761 0.435243726 0.6376540939
## 1113 -0.53766568 0.911348651 -2.274236278 0.859954822 -0.4218320913
## 1114 -1.08654649 1.014537567 0.886917502 1.336664101 -0.0710198781
## 1117 3.94985233 -1.716359994 -0.641719964 -0.264276341 0.8567586597
## 1119 -1.02607514 -0.978030272 0.676910859 0.674289447 0.3920284395
## 1123 -0.40290712 0.785648739 1.155943955 -0.021246431 -1.1691012573
## 1125 0.51105853 -0.245840001 0.195980399 0.377499738 0.4724647807
## 1128 -1.31409528 -0.319871405 0.676900918 0.538684115 1.3296487361
## 1138 -0.85701556 -0.402144768 1.015452290 -1.801337794 0.8906035407
## 1139 1.68782662 -1.556740290 -0.300103991 0.269823635 -0.4689481934
## 1150 -0.47890333 -0.235324855 0.744283560 0.211736984 0.1442438079
## 1153 -0.99029732 0.006418909 0.900894666 -0.485086716 1.3897314717
## 1155 3.27981020 -0.122455337 -0.079720740 -0.383851203 1.3578370392
## 1156 -0.26447142 -0.945587037 0.202679447 -0.215468234 -0.7088216703
## 1161 0.29218650 -0.859800419 -0.163904973 -0.497450969 -0.0356847783
## 1167 2.38340587 -0.906554973 -0.249745832 1.453664169 0.8414983923
## 1169 -0.74948837 -0.055476018 0.988541854 -0.407129342 0.4341339074
## 1171 -1.16193265 -0.153610151 0.616256544 0.187084939 1.6029160458
## 1172 -0.85234999 1.046496461 -1.818114337 -0.650465653 -1.8658661054
## 1187 -0.37330855 -0.836688899 -2.926665534 1.099408122 1.3393923955
## 1196 1.97449387 0.724870438 0.154980237 0.521648683 -0.0070421073
## 1200 -0.85470449 0.078257045 0.617160132 -1.082064111 0.0826835327
## 1201 -0.90848917 -0.512845396 -0.052551044 0.118554379 -0.2771893608
## 1202 -0.55881989 0.733094607 -1.906948332 -0.426831779 1.3579036478
## 1211 -0.71135786 -1.113795382 0.469933212 -0.487163002 -0.7658725831
## 1219 1.00211827 -0.527787938 0.094957403 0.341964203 0.3444357469
## 1220 -2.36958769 1.318793961 0.664422393 0.950191016 1.3745582556
## 1244 0.63686737 -0.072893854 -0.004184601 0.861099887 -0.3271630301
## 1245 -0.09223212 -0.394525109 0.632826399 2.006330322 -0.1233382652
## 1253 -0.42348838 -1.659621429 -0.012599247 1.163239747 0.9215912625
## 1254 -1.65405755 2.258022915 0.977681614 0.356666380 0.5496384464
## 1260 -0.52936713 -0.217004991 0.548776249 -0.106260244 0.7882381696
## 1266 -1.48925268 1.112994231 0.791362009 0.181870519 0.2030315648
## 1270 -0.01095539 -1.711741310 -0.095184057 0.131911504 -0.7006242109
## 1271 -0.79148066 0.745969303 0.445003428 -0.163262203 1.2030869534
## 1273 -0.35069960 -0.592198096 0.190379744 -0.364690824 -0.1099135763
## 1276 1.98413790 -0.309127205 0.099063479 0.208938919 -1.2186355928
## 1283 -1.60791374 0.934246935 0.682150296 1.311509022 -0.2133775823
## 1292 -0.07133452 0.476915382 -2.112324648 0.051305163 -0.2223116484
## 1304 -0.02498823 1.749196433 0.420815301 0.371476950 -0.6521043908
## 1308 -0.67872200 0.165448623 0.913062389 1.437175539 -0.5555965173
## 1311 2.90171492 -1.014307999 -0.307250180 -0.210209142 -1.2901585610
## 1313 -0.20083824 -0.963824992 -2.447456872 1.493647219 0.1156611242
## 1330 -0.83945069 0.307354094 0.773393347 -0.468190072 -0.0783363579
## 1331 2.15001966 1.974358369 0.743969906 0.462189144 0.4449896958
## 1334 0.10491643 0.894574891 -2.559751834 0.023052782 -0.7523249302
## 1340 -0.93987414 0.969687358 -1.744902764 -0.159899755 0.7404762311
## 1345 -1.03495768 0.618041754 0.511119055 1.270974152 -0.5198447590
## 1347 0.71576110 -1.572276548 -0.023967718 -2.758394977 -0.3976254910
## 1355 0.28733231 -1.906936971 -3.363334478 -2.593574367 -1.9850384612
## 1358 0.33265796 2.419464057 0.683745576 1.301228864 -0.4859515045
## 1360 0.04748913 1.016177087 0.675830244 -1.293325367 1.2981447013
## 1362 -0.71901647 -1.225017103 0.450688514 0.523935923 1.1415258202
## 1364 -0.01661860 -0.765553826 0.561731922 0.285310986 0.2949393535
## 1366 -0.86284507 -0.324519745 -2.135698875 -0.243419508 -0.4409514021
## 1371 -1.00178822 0.331984988 -0.028255561 0.712416255 -1.0260555598
## 1377 -0.23889689 -1.032796573 0.081468063 -0.221637330 -0.2251706609
## 1380 -0.50449543 -0.429782385 -1.977405358 -0.199835627 -0.2750240893
## 1387 -0.71464969 0.222376085 1.112701563 0.929106095 -0.3663795387
## 1389 -0.56034839 -0.180519831 0.348968514 0.345529963 1.5311545940
## 1390 -0.28870446 0.228248307 0.736748943 1.379959439 -0.3230939241
## 1392 -1.15934931 0.860641899 0.971551179 0.348507151 -1.9697039864
## 1400 0.75672839 -1.052782224 0.198814423 -0.214661527 -1.0352559478
## 1407 -0.68791138 0.476326592 0.031460368 -0.313599967 -2.4720516907
## 1411 -0.26365009 0.440279649 0.585626546 0.048548310 -1.2861282114
## 1417 0.01943097 -1.027251813 0.160513593 1.529878390 -0.3754176159
## 1420 -0.77818757 0.849966001 0.472395659 -0.283078077 -0.5492524925
## 1423 -1.83537770 0.406258795 0.317447876 0.575868695 0.7186816610
## 1430 -1.30144620 0.544123330 0.484187860 -2.677052272 -0.3400302859
## 1434 -0.21417598 -0.139548887 1.116756515 -0.559627990 0.2249108069
## 1435 0.04846469 -2.292120087 -0.403633596 -2.167038749 -1.1917806707
## 1443 -1.78048187 1.380364499 -2.088320240 2.012352403 1.0112815557
## 1445 -1.43648785 1.797500246 -2.704608681 -2.361978302 -1.0441136566
## 1455 -1.20630732 0.589328865 0.032161347 -1.069897300 0.0378960737
## 1462 1.34429149 0.595312143 -2.758826337 -1.088343131 -0.7786121171
## 1463 1.88928554 -0.420583916 0.449550416 -2.883713691 0.6184707331
## 1467 0.44730610 1.788808018 0.799554435 -0.474161278 -0.6278729056
## 1468 -0.09309528 -0.006137157 0.924846250 1.123047993 0.0146421166
## 1470 -0.43010057 -0.906359633 0.294960226 0.851976958 -0.2990289650
## LD6 LD7 LD8 LD9
## 4 1.055790937 0.491458942 -0.524857751 0.153641184
## 5 -1.559413505 -1.343932045 0.463923580 0.673128280
## 9 -0.360148209 0.940561487 -1.095300797 -0.596338928
## 15 -1.065557024 -0.124321025 -0.743828381 -1.074279216
## 20 1.060563933 -0.876213292 -1.025293345 0.893321045
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## 1058 0.079138388 0.027427752 2.250415583 -1.678860418
## 1060 0.159309518 0.883077761 -0.809743699 1.730097353
## 1062 -0.482880742 1.588783887 -0.717927051 0.124493518
## 1064 -0.959121886 0.519321029 -0.213624965 -0.690462978
## 1065 -0.478643591 0.261001289 -0.419942261 1.297135936
## 1067 -0.569197247 -1.707311870 0.407155557 -1.036688219
## 1068 1.191223598 -0.264847008 -0.216852000 -0.396901984
## 1071 -0.429361456 1.685042747 0.089602244 -0.272548571
## 1072 0.397282019 0.373398915 -0.916870999 0.843781571
## 1080 -0.441161112 -0.358565604 0.085822500 -0.097045697
## 1081 -0.978292848 -1.102880039 -1.604336544 0.347463807
## 1084 2.446186484 1.690990621 0.320854239 -1.517449895
## 1091 -1.317748094 1.390866041 -0.244929481 0.541207002
## 1092 -0.531678993 1.304673644 -1.316591911 -1.144605121
## 1102 0.021555411 0.966196220 -0.835594550 0.673614876
## 1103 1.804664384 -0.735996011 0.577690177 -0.101539736
## 1113 0.214153613 0.280119579 -0.223085620 0.518890806
## 1114 1.594678383 1.168881968 -0.159291362 -1.031586308
## 1117 -0.085329059 -0.768809277 -0.871272183 -1.626013234
## 1119 -0.619702587 -0.952296045 1.522690989 0.641221794
## 1123 -1.157351451 1.294606981 0.622591735 1.086679758
## 1125 0.575937280 0.368431442 -0.820522186 0.512770342
## 1128 0.004649243 0.713828864 -0.599595057 -0.083570051
## 1138 -1.110332834 0.609504610 0.929284966 -1.202185331
## 1139 -0.092332153 -0.915371439 -0.304656073 -1.614838553
## 1150 -0.623595948 1.957536118 -1.008383226 -1.154376550
## 1153 -0.715887227 0.326312455 0.388202887 1.698407834
## 1155 -0.476640326 0.101177765 -1.540656010 -1.616894126
## 1156 0.373977588 0.424208367 -0.049189048 1.518108241
## 1161 1.074051090 -0.025819727 -0.778280494 1.978739901
## 1167 0.934027348 -0.989897413 -0.142717586 -0.227238268
## 1169 -1.307481848 -0.583951261 1.608914435 1.828748901
## 1171 1.560873837 0.279584745 0.345987750 0.420732926
## 1172 1.002434117 0.590955627 2.165310981 -1.005635339
## 1187 -0.304747751 -0.394048063 -1.503721795 0.313527674
## 1196 0.406721416 -0.645831524 -0.419518549 0.759425589
## 1200 -0.582209234 -1.505417448 0.641040049 -2.572464823
## 1201 1.027941374 -1.254083436 -0.487339629 1.146021444
## 1202 -0.663468888 1.525719153 -0.212166683 1.518972692
## 1211 -1.037753136 0.418118105 -0.040165915 -0.966059467
## 1219 0.626637223 0.547880810 -0.746801703 0.630185777
## 1220 0.423330324 -1.093337037 -1.492844470 -1.053040575
## 1244 -0.466011897 -0.855970734 -1.252018336 1.000070472
## 1245 0.601974545 1.873092037 -0.380767574 -0.384388255
## 1253 1.299678055 0.148710340 -0.337538472 0.622332162
## 1254 1.314097938 -0.079180428 -0.599207565 -0.542914104
## 1260 -0.602801463 -0.014708877 -0.451697337 -0.550958610
## 1266 1.391948398 0.541522738 -0.380129468 -0.397016036
## 1270 0.563236968 -0.764494303 0.568279517 1.297524345
## 1271 0.430770630 -0.580622518 -0.906990184 1.275606409
## 1273 0.543261886 0.674983446 -0.813675933 1.256629882
## 1276 -0.273008275 -1.122630321 0.820487852 0.725135062
## 1283 0.439112124 0.496244747 -1.391320173 -1.201997129
## 1292 2.164775008 2.248468499 0.660383958 -1.544530309
## 1304 0.259357480 -1.002339405 -1.100946740 -0.034122376
## 1308 -0.070179775 1.414016648 0.143849227 0.101256465
## 1311 -0.436424094 -1.345624467 0.294250325 -0.604523266
## 1313 0.111874055 2.034056940 -0.751221860 -1.861953425
## 1330 -0.221288816 1.574198137 -0.650858957 1.347671653
## 1331 -1.251998504 -1.856628928 0.566331266 -0.240406006
## 1334 0.018434276 -0.066317780 -0.791644605 0.025260215
## 1340 -0.700981382 2.046973116 -0.257790105 1.306211167
## 1345 0.623655960 0.618556791 -1.344197678 -0.961931169
## 1347 -0.036540900 -0.275388871 0.498531250 -0.206529314
## 1355 -0.722288805 -1.217205130 0.083757789 0.728041641
## 1358 -1.268959616 -0.725823315 -1.842494716 -0.283400254
## 1360 0.942742358 0.266810402 0.063985057 1.547399670
## 1362 0.061348867 0.112461829 0.347177069 0.652583117
## 1364 0.582963353 -0.015417839 1.228710118 -1.009030514
## 1366 -1.154244316 1.748038676 -0.495777349 -1.270661109
## 1371 -0.551561214 -1.414817069 -2.246688314 -0.806279856
## 1377 -1.269420710 -1.090970439 -0.447126781 1.526465743
## 1380 -1.961192147 0.472390395 0.950120355 -1.079845705
## 1387 0.769824223 1.905447960 1.022903837 -0.310701056
## 1389 -0.174238974 -1.152438381 -0.573537592 -0.932032638
## 1390 0.405052789 1.770009129 -0.516244685 0.230821972
## 1392 0.408055696 -0.107880774 1.396235494 -0.477867324
## 1400 -0.691489044 -0.747263722 0.782871635 0.126276900
## 1407 0.534229116 -0.307404037 -1.513016062 -0.287989894
## 1411 -0.290348857 -0.094787900 0.206889856 0.953141232
## 1417 1.182081914 1.114788167 -0.539672478 0.197780118
## 1420 1.089843185 0.579970400 -1.228464224 -2.181961496
## 1423 0.653833020 -0.819499664 -1.531435284 -0.864730961
## 1430 -1.847283694 -2.162527525 -0.255642502 0.136500523
## 1434 -0.598621696 0.273341645 2.193545001 0.141013185
## 1435 0.316933196 -1.620169135 0.513631976 -1.706607116
## 1443 -1.413436766 -2.817448167 0.181669275 0.212198300
## 1445 2.889123930 -0.590958350 -0.575466816 0.405022842
## 1455 0.243190208 -1.075142354 -2.228413731 -0.771456186
## 1462 -0.599340002 1.138538065 -1.987256430 -1.359580137
## 1463 -0.896940690 0.135918291 0.844945217 0.189488183
## 1467 -0.371715456 1.310229525 -1.199439044 0.939483906
## 1468 -0.706467187 0.563918463 0.811828553 0.020315514
## 1470 -1.240034623 -0.612341309 -0.344309854 0.611334554
# Get the posteriors as a dataframe.
attr_raw.lda.predict.posteriors <- as.data.frame(attr_raw.lda.predict$posterior)
# Map numeric values to categorical labels
test_raw.df$Attrition <- ifelse(test_raw.df$Attrition == 0, "No", "Yes")
pred <- prediction(attr_raw.lda.predict.posteriors[,5], test_raw.df$Attrition)
roc.perf = performance(pred, measure = "tpr", x.measure = "fpr")
auc.train <- performance(pred, measure = "auc")
auc.train <- auc.train@y.values
plot(roc.perf)
abline(a=0, b= 1)
text(x = .25, y = .65 ,paste("AUC = ", round(auc.train[[1]],3), sep = ""))
#Inference: #Lower AUC score indicates model performance is not good.
# Iris LDA
data("iris")
iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginica
head(iris, 3)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
str(iris)
## 'data.frame': 150 obs. of 5 variables:
## $ Sepal.Length: num 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
## $ Sepal.Width : num 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
## $ Petal.Length: num 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
## $ Petal.Width : num 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
## $ Species : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
r <- lda(formula = Species ~ ., data = iris)
r
## Call:
## lda(Species ~ ., data = iris)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026
##
## Coefficients of linear discriminants:
## LD1 LD2
## Sepal.Length 0.8293776 -0.02410215
## Sepal.Width 1.5344731 -2.16452123
## Petal.Length -2.2012117 0.93192121
## Petal.Width -2.8104603 -2.83918785
##
## Proportion of trace:
## LD1 LD2
## 0.9912 0.0088
summary(r)
## Length Class Mode
## prior 3 -none- numeric
## counts 3 -none- numeric
## means 12 -none- numeric
## scaling 8 -none- numeric
## lev 3 -none- character
## svd 2 -none- numeric
## N 1 -none- numeric
## call 3 -none- call
## terms 3 terms call
## xlevels 0 -none- list
print(r)
## Call:
## lda(Species ~ ., data = iris)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026
##
## Coefficients of linear discriminants:
## LD1 LD2
## Sepal.Length 0.8293776 -0.02410215
## Sepal.Width 1.5344731 -2.16452123
## Petal.Length -2.2012117 0.93192121
## Petal.Width -2.8104603 -2.83918785
##
## Proportion of trace:
## LD1 LD2
## 0.9912 0.0088
r$counts
## setosa versicolor virginica
## 50 50 50
r$means
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026
r$scaling
## LD1 LD2
## Sepal.Length 0.8293776 -0.02410215
## Sepal.Width 1.5344731 -2.16452123
## Petal.Length -2.2012117 0.93192121
## Petal.Width -2.8104603 -2.83918785
r$prior
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
r$lev
## [1] "setosa" "versicolor" "virginica"
r$svd
## [1] 48.642644 4.579983
#singular values (svd) that gives the ratio of the between- and within-group standard deviations on the linear discriminant variables.
r$N
## [1] 150
r$call
## lda(formula = Species ~ ., data = iris)
(prop = r$svd^2/sum(r$svd^2))
## [1] 0.991212605 0.008787395
#we can use the singular values to compute the amount of the between-group variance that is explained by each linear discriminant. In our example we see that the first linear discriminant explains more than 99% of the between-group variance in the iris dataset.
r2 <- lda(formula = Species ~ ., data = iris, CV = TRUE)
r2
## $class
## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginica
##
## $posterior
## setosa versicolor virginica
## 1 1.000000e+00 5.087494e-22 4.385241e-42
## 2 1.000000e+00 9.588256e-18 8.888069e-37
## 3 1.000000e+00 1.983745e-19 8.606982e-39
## 4 1.000000e+00 1.505573e-16 5.101765e-35
## 5 1.000000e+00 2.075670e-22 1.739832e-42
## 6 1.000000e+00 5.332271e-21 8.674906e-40
## 7 1.000000e+00 1.498839e-18 3.999205e-37
## 8 1.000000e+00 5.268133e-20 1.983027e-39
## 9 1.000000e+00 2.280729e-15 1.293376e-33
## 10 1.000000e+00 1.504085e-18 5.037348e-38
## 11 1.000000e+00 1.296140e-23 4.023338e-44
## 12 1.000000e+00 2.171874e-18 3.223111e-37
## 13 1.000000e+00 1.996136e-18 6.109118e-38
## 14 1.000000e+00 1.604055e-19 2.549802e-39
## 15 1.000000e+00 2.843397e-31 1.593594e-54
## 16 1.000000e+00 2.330545e-28 3.074132e-49
## 17 1.000000e+00 5.136116e-25 3.269819e-45
## 18 1.000000e+00 5.747697e-21 2.253825e-40
## 19 1.000000e+00 2.187125e-22 4.069438e-42
## 20 1.000000e+00 3.297882e-22 9.802494e-42
## 21 1.000000e+00 1.757286e-19 8.150916e-39
## 22 1.000000e+00 2.027767e-20 3.730752e-39
## 23 1.000000e+00 5.650696e-25 6.509776e-46
## 24 1.000000e+00 8.618517e-15 7.014744e-32
## 25 1.000000e+00 1.520334e-15 1.857885e-33
## 26 1.000000e+00 2.936141e-16 8.159510e-35
## 27 1.000000e+00 4.557392e-17 5.510803e-35
## 28 1.000000e+00 2.079675e-21 2.831513e-41
## 29 1.000000e+00 1.232321e-21 1.082692e-41
## 30 1.000000e+00 1.153050e-16 4.267126e-35
## 31 1.000000e+00 2.584595e-16 9.537258e-35
## 32 1.000000e+00 2.878754e-19 5.473623e-38
## 33 1.000000e+00 2.247070e-27 4.047137e-49
## 34 1.000000e+00 2.620949e-29 1.970538e-51
## 35 1.000000e+00 1.493279e-17 2.047516e-36
## 36 1.000000e+00 2.146308e-21 1.550216e-41
## 37 1.000000e+00 1.673983e-24 1.322398e-45
## 38 1.000000e+00 3.810942e-23 9.131835e-44
## 39 1.000000e+00 5.423320e-17 1.146137e-35
## 40 1.000000e+00 2.414191e-20 6.552342e-40
## 41 1.000000e+00 1.417602e-21 3.569675e-41
## 42 1.000000e+00 8.956712e-11 4.968454e-28
## 43 1.000000e+00 2.125837e-18 2.395462e-37
## 44 1.000000e+00 1.101293e-15 1.403899e-32
## 45 1.000000e+00 2.285363e-17 5.214629e-35
## 46 1.000000e+00 2.087086e-16 1.027948e-34
## 47 1.000000e+00 2.588201e-22 3.634491e-42
## 48 1.000000e+00 3.643000e-18 4.504970e-37
## 49 1.000000e+00 3.000767e-23 1.346233e-43
## 50 1.000000e+00 3.171862e-20 7.860312e-40
## 51 3.157725e-18 9.998716e-01 1.284247e-04
## 52 1.753919e-19 9.991816e-01 8.184018e-04
## 53 2.551962e-22 9.951044e-01 4.895626e-03
## 54 2.742687e-22 9.995996e-01 4.004477e-04
## 55 4.854978e-23 9.951404e-01 4.859638e-03
## 56 9.575747e-23 9.982973e-01 1.702702e-03
## 57 4.467689e-22 9.838631e-01 1.613691e-02
## 58 5.922943e-14 9.999999e-01 8.584221e-08
## 59 8.088509e-20 9.998655e-01 1.344590e-04
## 60 1.767441e-20 9.994314e-01 5.686054e-04
## 61 3.330661e-18 9.999987e-01 1.314516e-06
## 62 8.331100e-20 9.991631e-01 8.369389e-04
## 63 4.614428e-18 9.999989e-01 1.117671e-06
## 64 1.290071e-23 9.939163e-01 6.083745e-03
## 65 5.229707e-14 9.999984e-01 1.593028e-06
## 66 3.393529e-17 9.999528e-01 4.721492e-05
## 67 7.983370e-24 9.763990e-01 2.360097e-02
## 68 3.119288e-16 9.999991e-01 8.659241e-07
## 69 3.847473e-28 9.390462e-01 6.095377e-02
## 70 1.678698e-17 9.999966e-01 3.360127e-06
## 71 1.302246e-28 1.772727e-01 8.227273e-01
## 72 1.113263e-16 9.999902e-01 9.801197e-06
## 73 1.634947e-29 7.868347e-01 2.131653e-01
## 74 3.331093e-22 9.995073e-01 4.926830e-04
## 75 1.013127e-17 9.999741e-01 2.594176e-05
## 76 2.949236e-18 9.999081e-01 9.193549e-05
## 77 7.224891e-23 9.979459e-01 2.054146e-03
## 78 2.386376e-27 6.569495e-01 3.430505e-01
## 79 4.473658e-23 9.922840e-01 7.716012e-03
## 80 7.145460e-12 1.000000e+00 1.241414e-08
## 81 1.333306e-17 9.999970e-01 3.044209e-06
## 82 1.119894e-15 9.999997e-01 2.916503e-07
## 83 1.748156e-16 9.999961e-01 3.876682e-06
## 84 1.125494e-33 9.924153e-02 9.007585e-01
## 85 1.191672e-24 9.474667e-01 5.253333e-02
## 86 1.983291e-20 9.924721e-01 7.527887e-03
## 87 4.531906e-21 9.980100e-01 1.989996e-03
## 88 2.035626e-23 9.993358e-01 6.642410e-04
## 89 7.813451e-18 9.999440e-01 5.603286e-05
## 90 8.212308e-21 9.998033e-01 1.967487e-04
## 91 6.631189e-23 9.992802e-01 7.197827e-04
## 92 7.049062e-22 9.979525e-01 2.047473e-03
## 93 4.490728e-18 9.999881e-01 1.188058e-05
## 94 2.600275e-14 9.999999e-01 8.745690e-08
## 95 6.422939e-21 9.996751e-01 3.248823e-04
## 96 2.159263e-17 9.999804e-01 1.956029e-05
## 97 3.823305e-19 9.998801e-01 1.199041e-04
## 98 2.089502e-18 9.999504e-01 4.963639e-05
## 99 9.013113e-11 1.000000e+00 9.943306e-09
## 100 6.167377e-19 9.999219e-01 7.813051e-05
## 101 1.335977e-53 3.188548e-09 1.000000e+00
## 102 9.949508e-38 1.209398e-03 9.987906e-01
## 103 1.950796e-42 2.774428e-05 9.999723e-01
## 104 3.081602e-38 1.232592e-03 9.987674e-01
## 105 5.411117e-46 1.807449e-06 9.999982e-01
## 106 5.887455e-50 5.662591e-07 9.999994e-01
## 107 1.203272e-32 8.794800e-02 9.120520e-01
## 108 1.774038e-42 1.735541e-04 9.998264e-01
## 109 1.924345e-42 2.617818e-04 9.997382e-01
## 110 1.851248e-46 1.352651e-07 9.999999e-01
## 111 4.379051e-32 1.446014e-02 9.855399e-01
## 112 2.052671e-37 1.776421e-03 9.982236e-01
## 113 9.704392e-39 2.172029e-04 9.997828e-01
## 114 2.386650e-40 2.251253e-04 9.997749e-01
## 115 8.048237e-46 8.410965e-07 9.999992e-01
## 116 1.008588e-39 2.840103e-05 9.999716e-01
## 117 2.811294e-35 6.595206e-03 9.934048e-01
## 118 7.282186e-45 1.296566e-06 9.999987e-01
## 119 1.004644e-64 2.647509e-10 1.000000e+00
## 120 3.160887e-33 3.033047e-01 6.966953e-01
## 121 1.719583e-42 6.688965e-06 9.999933e-01
## 122 6.252717e-37 9.870164e-04 9.990130e-01
## 123 2.627103e-51 7.704580e-07 9.999992e-01
## 124 1.504499e-31 1.070121e-01 8.929879e-01
## 125 3.688147e-39 9.571422e-05 9.999043e-01
## 126 2.426533e-36 3.398007e-03 9.966020e-01
## 127 3.865436e-30 2.055755e-01 7.944245e-01
## 128 3.606381e-30 1.437670e-01 8.562330e-01
## 129 8.371636e-44 1.376281e-05 9.999862e-01
## 130 2.937738e-32 1.589920e-01 8.410080e-01
## 131 6.294581e-42 1.714027e-04 9.998286e-01
## 132 5.466934e-36 7.736441e-04 9.992264e-01
## 133 1.208158e-45 3.051435e-06 9.999969e-01
## 134 5.464475e-29 7.876238e-01 2.123762e-01
## 135 9.884011e-35 1.578198e-01 8.421802e-01
## 136 6.515088e-46 1.990735e-06 9.999980e-01
## 137 2.840394e-44 7.895048e-07 9.999992e-01
## 138 7.160822e-35 7.053731e-03 9.929463e-01
## 139 1.782247e-29 2.122042e-01 7.877958e-01
## 140 3.640914e-36 9.289807e-04 9.990710e-01
## 141 5.881132e-45 1.108009e-06 9.999989e-01
## 142 2.122304e-35 6.157433e-04 9.993843e-01
## 143 9.949508e-38 1.209398e-03 9.987906e-01
## 144 9.585800e-46 9.978596e-07 9.999990e-01
## 145 2.206003e-46 2.038879e-07 9.999998e-01
## 146 1.133074e-38 8.851900e-05 9.999115e-01
## 147 8.781586e-36 7.084468e-03 9.929155e-01
## 148 7.108984e-35 3.342993e-03 9.966570e-01
## 149 3.096565e-40 1.338572e-05 9.999866e-01
## 150 3.585667e-33 2.058806e-02 9.794119e-01
##
## $terms
## Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width
## attr(,"variables")
## list(Species, Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)
## attr(,"factors")
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Species 0 0 0 0
## Sepal.Length 1 0 0 0
## Sepal.Width 0 1 0 0
## Petal.Length 0 0 1 0
## Petal.Width 0 0 0 1
## attr(,"term.labels")
## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
## attr(,"order")
## [1] 1 1 1 1
## attr(,"intercept")
## [1] 1
## attr(,"response")
## [1] 1
## attr(,".Environment")
## <environment: R_GlobalEnv>
## attr(,"predvars")
## list(Species, Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)
## attr(,"dataClasses")
## Species Sepal.Length Sepal.Width Petal.Length Petal.Width
## "factor" "numeric" "numeric" "numeric" "numeric"
##
## $call
## lda(formula = Species ~ ., data = iris, CV = TRUE)
##
## $xlevels
## named list()
head(r2$class)
## [1] setosa setosa setosa setosa setosa setosa
## Levels: setosa versicolor virginica
#the Maximum a Posteriori Probability (MAP) classification (a factor)
#posterior: posterior probabilities for the classes.
head(r2$posterior, 3)
## setosa versicolor virginica
## 1 1 5.087494e-22 4.385241e-42
## 2 1 9.588256e-18 8.888069e-37
## 3 1 1.983745e-19 8.606982e-39
train <- sample(1:150, 75)
r3 <- lda(Species ~ ., # training model
iris,
prior = c(1,1,1)/3,
subset = train)
plda = predict(object = r3, # predictions
newdata = iris[-train, ])
head(plda$class)
## [1] setosa setosa setosa setosa setosa setosa
## Levels: setosa versicolor virginica
head(plda$posterior, 6) # posterior prob.
## setosa versicolor virginica
## 6 1 3.209060e-20 2.483820e-38
## 7 1 8.120739e-18 1.075205e-35
## 9 1 4.370477e-15 1.013998e-32
## 10 1 1.683804e-18 1.605808e-37
## 13 1 2.294401e-18 2.152555e-37
## 14 1 4.506741e-19 3.002408e-38
head(plda$x, 3)
## LD1 LD2
## 6 7.517248 -1.5730027
## 7 7.029720 -0.4482425
## 9 6.478778 0.8606600
plot(r)
plot(r3)
r <- lda(Species ~ .,
iris,
prior = c(1,1,1)/3)
prop.lda = r$svd^2/sum(r$svd^2)
plda <- predict(object = r,
newdata = iris)
dataset = data.frame(species = iris[,"Species"],lda = plda$x)
ggplot(dataset) + geom_point(aes(lda.LD1, lda.LD2, colour = species, shape = species), size = 2.5) + labs(x = paste("LD1 (", percent(prop.lda[1]), ")", sep=""),y = paste("LD2 (", percent(prop.lda[2]), ")", sep=""))
#LDA is likely a good dimensionality reduction technique for this dataset, as it has been able to project the higher-dimensional data (four features: sepal length, sepal width, petal length, and petal width) onto a two-dimensional space (the plane of the scatter plot) while still maintaining some separability between the classes.
#The petal length appears to be a more important feature for classification than the sepal width, since the data points are more separated along the petal length axis.
# lets look at another way to divide a dataset
set.seed(101) # Nothing is random!!
sample_n(iris,10)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 6.3 2.5 4.9 1.5 versicolor
## 2 6.3 3.3 4.7 1.6 versicolor
## 3 5.6 2.7 4.2 1.3 versicolor
## 4 6.5 3.0 5.2 2.0 virginica
## 5 5.0 2.0 3.5 1.0 versicolor
## 6 6.6 2.9 4.6 1.3 versicolor
## 7 5.1 2.5 3.0 1.1 versicolor
## 8 6.1 3.0 4.9 1.8 virginica
## 9 7.4 2.8 6.1 1.9 virginica
## 10 5.4 3.4 1.5 0.4 setosa
# Lets take a sample of 75/25 like before. Dplyr preserves class.
training_sample <- sample(c(TRUE, FALSE), nrow(iris), replace = T, prob = c(0.75,0.25))
train <- iris[training_sample, ]
test <- iris[!training_sample, ]
#lets run LDA like before
lda.iris <- lda(Species ~ ., train)
# do a quick plot to understand how good the model is
plot(lda.iris, col = as.integer(train$Species))
# Sometime bell curves are better
plot(lda.iris, dimen = 1, type = "b")
# THis plot shows the essense of LDA. It puts everything on a line and finds cutoffs.
#Here are some of the things that can be inferred from the confusion matrix:
#Out of 140 employees, 95 did not leave (no attrition) and 45 left (attrition).
#The model correctly predicted 90 out of the 95 employees who did not leave (no attrition). This is called the true negative rate.
#The model correctly predicted 25 out of the 45 employees who left (attrition). This is called the true positive rate.
#There were 5 false positives, which means that the model predicted that 5 employees would leave (attrition) when they actually did not.
#There were 10 false negatives, which means that the model predicted that 10 employees would not leave (no attrition) when they actually did leave (attrition).
# Partition plots
partimat(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data=train, method="lda")
# Lets focus on accuracy. Table function
lda.train <- predict(lda.iris)
train$lda <- lda.train$class
table(train$lda,train$Species)
##
## setosa versicolor virginica
## setosa 35 0 0
## versicolor 0 30 1
## virginica 0 2 37
# running accuracy on the training set shows how good the model is. It is not an indication of "true" accuracy. We will use the test set to approximate accuracy
lda.test <- predict(lda.iris,test)
test$lda <- lda.test$class
table(test$lda,test$Species)
##
## setosa versicolor virginica
## setosa 15 0 0
## versicolor 0 18 0
## virginica 0 0 12
# Wilk's Lambda and F test for each variablw
m <- manova(cbind(Sepal.Length,Sepal.Width,Petal.Length,Petal.Width)~Species,data=iris)
summary(m,test="Wilks")
## Df Wilks approx F num Df den Df Pr(>F)
## Species 2 0.023439 199.15 8 288 < 2.2e-16 ***
## Residuals 147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(m,test="Pillai")
## Df Pillai approx F num Df den Df Pr(>F)
## Species 2 1.1919 53.466 8 290 < 2.2e-16 ***
## Residuals 147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(m)
## Response Sepal.Length :
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 2 63.212 31.606 119.26 < 2.2e-16 ***
## Residuals 147 38.956 0.265
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Sepal.Width :
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 2 11.345 5.6725 49.16 < 2.2e-16 ***
## Residuals 147 16.962 0.1154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Petal.Length :
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 2 437.10 218.551 1180.2 < 2.2e-16 ***
## Residuals 147 27.22 0.185
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Petal.Width :
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 2 80.413 40.207 960.01 < 2.2e-16 ***
## Residuals 147 6.157 0.042
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Inference:
#Specifically, the plot shows three partition plots, each representing a different app error rate. The petal length and sepal width are on the x and y axes. The color regions correspond to the predicted class label for a given data point. In the top left plot, where the app error rate is 0.2, the data points in blue are classified as belonging to class 1, the green points are classified as class 2, and the yellow points are classified as class 3.
#From the plot, we can see that the model performs better when the petal length and sepal width are more distinct between the classes. In the top left plot (where the error rate is highest), the classes are more overlapping than in the bottom right plot (where the error rate is lowest). This suggests that the model is more confident in its predictions when the data points are clearly separated in terms of petal length and sepal width.